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Lớp 9

Tính $ \sqrt{45.80}$

$ \sqrt{45.80}=\sqrt{3600}=60$

https://khoahoc.vietjack.com/question/1008443

### Câu hỏi: Tính  <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>45.80</mn></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>45.80</mn></msqrt><mo>=</mo><msqrt><mn>3600</mn></msqrt><mo>=</mo><mn>60</mn></math>

Free Form

Lớp 9

Tính $ \sqrt{2,5.14,4}$

$ \sqrt{2,5.14,4}=\sqrt{36}=6$

https://khoahoc.vietjack.com/question/1008445

### Câu hỏi: Tính  <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn><mo>,</mo><mn>5.14</mn><mo>,</mo><mn>4</mn></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn><mo>,</mo><mn>5.14</mn><mo>,</mo><mn>4</mn></msqrt><mo>=</mo><msqrt><mn>36</mn></msqrt><mo>=</mo><mn>6</mn></math>

Free Form

Lớp 9

Tính $ \sqrt{21,{8}^{2}-18,{2}^{2}}$

$ \sqrt{21,{8}^{2}-18,{2}^{2}}=\sqrt{\left(21,8-18,2\right)\left(21,8+18,2\right)}=\sqrt{3,6.40}=\sqrt{144}=12$

https://khoahoc.vietjack.com/question/1008448

### Câu hỏi: Tính <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>21</mn><mo>,</mo><msup><mn>8</mn><mn>2</mn></msup><mo>−</mo><mn>18</mn><mo>,</mo><msup><mn>2</mn><mn>2</mn></msup></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>21</mn><mo>,</mo><msup><mn>8</mn><mn>2</mn></msup><mo>−</mo><mn>18</mn><mo>,</mo><msup><mn>2</mn><mn>2</mn></msup></msqrt><mo>=</mo><msqrt><mfenced><mrow><mn>21</mn><mo>,</mo><mn>8</mn><mo>−</mo><mn>18</mn><mo>,</mo><mn>2</mn></mrow></mfenced><mfenced><mrow><mn>21</mn><mo>,</mo><mn>8</mn><mo>+</mo><mn>18</mn><mo>,</mo><mn>2</mn></mrow></mfenced></msqrt><mo>=</mo><msqrt><mn>3</mn><mo>,</mo><mn>6.40</mn></msqrt><mo>=</mo><msqrt><mn>144</mn></msqrt><mo>=</mo><mn>12</mn></math>

Free Form

Lớp 9

<p>Tính</p> <p>$ \sqrt{117,{5}^{2}-26,{5}^{2}-1440}$</p>

$ \begin{array}{l}\sqrt{117,{5}^{2}-26,{5}^{2}-1440}=\sqrt{\left(117,5-26,5\right)\left(117,5+26,5\right)-1440}\\ =\sqrt{91.144-10.144}=\sqrt{81.144}=\sqrt{81}.\sqrt{144}=9.12=108\end{array}$ <div> </div>

https://khoahoc.vietjack.com/question/1008451

### Câu hỏi: <p>Tính</p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>117</mn><mo>,</mo><msup><mn>5</mn><mn>2</mn></msup><mo>−</mo><mn>26</mn><mo>,</mo><msup><mn>5</mn><mn>2</mn></msup><mo>−</mo><mn>1440</mn></msqrt></math></p> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>117</mn><mo>,</mo><msup><mn>5</mn><mn>2</mn></msup><mo>−</mo><mn>26</mn><mo>,</mo><msup><mn>5</mn><mn>2</mn></msup><mo>−</mo><mn>1440</mn></msqrt><mo>=</mo><msqrt><mfenced><mrow><mn>117</mn><mo>,</mo><mn>5</mn><mo>−</mo><mn>26</mn><mo>,</mo><mn>5</mn></mrow></mfenced><mfenced><mrow><mn>117</mn><mo>,</mo><mn>5</mn><mo>+</mo><mn>26</mn><mo>,</mo><mn>5</mn></mrow></mfenced><mo>−</mo><mn>1440</mn></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>91.144</mn><mo>−</mo><mn>10.144</mn></msqrt><mo>=</mo><msqrt><mn>81.144</mn></msqrt><mo>=</mo><msqrt><mn>81</mn></msqrt><mo>.</mo><msqrt><mn>144</mn></msqrt><mo>=</mo><mn>9.12</mn><mo>=</mo><mn>108</mn></mtd></mtr></mtable></math> <div> </div>

Free Form

Lớp 9

Tính $ \sqrt{146,{5}^{2}-109,{5}^{2}+27.256}$

$ \begin{array}{l}\sqrt{146,{5}^{2}-109,{5}^{2}+27.256}\\ =\sqrt{\left(146,5-109,5\right).\left(146,5+109,5\right)+27.256}\\ =\sqrt{37.256+27.256}=\sqrt{\left(37+27\right).256}\\ =\sqrt{64.256}=\sqrt{64}.\sqrt{256}=8.16=128\end{array}$

https://khoahoc.vietjack.com/question/1008453

### Câu hỏi: Tính  <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>146</mn><mo>,</mo><msup><mn>5</mn><mn>2</mn></msup><mo>−</mo><mn>109</mn><mo>,</mo><msup><mn>5</mn><mn>2</mn></msup><mo>+</mo><mn>27.256</mn></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>146</mn><mo>,</mo><msup><mn>5</mn><mn>2</mn></msup><mo>−</mo><mn>109</mn><mo>,</mo><msup><mn>5</mn><mn>2</mn></msup><mo>+</mo><mn>27.256</mn></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mfenced><mrow><mn>146</mn><mo>,</mo><mn>5</mn><mo>−</mo><mn>109</mn><mo>,</mo><mn>5</mn></mrow></mfenced><mo>.</mo><mfenced><mrow><mn>146</mn><mo>,</mo><mn>5</mn><mo>+</mo><mn>109</mn><mo>,</mo><mn>5</mn></mrow></mfenced><mo>+</mo><mn>27.256</mn></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>37.256</mn><mo>+</mo><mn>27.256</mn></msqrt><mo>=</mo><msqrt><mfenced><mrow><mn>37</mn><mo>+</mo><mn>27</mn></mrow></mfenced><mn>.256</mn></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>64.256</mn></msqrt><mo>=</mo><msqrt><mn>64</mn></msqrt><mo>.</mo><msqrt><mn>256</mn></msqrt><mo>=</mo><mn>8.16</mn><mo>=</mo><mn>128</mn></mtd></mtr></mtable></math>

Free Form

Lớp 9

<p>Tính</p> <p>$ \frac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}$</p>

<p>$ \frac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}=\frac{\sqrt{3}.\sqrt{2}+\sqrt{7}.\sqrt{2}}{2\sqrt{3}+2\sqrt{7}}=\frac{\sqrt{2}.\left(\sqrt{3}+\sqrt{7}\right)}{2\left(\sqrt{3}+\sqrt{7}\right)}=\frac{\sqrt{2}}{2}$</p>

https://khoahoc.vietjack.com/question/1008458

### Câu hỏi: <p>Tính</p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msqrt><mn>6</mn></msqrt><mo>+</mo><msqrt><mn>14</mn></msqrt></mrow><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt><mo>+</mo><msqrt><mn>28</mn></msqrt></mrow></mfrac><mo> </mo><mo> </mo><mo> </mo></math></p> ### Lời giải: <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msqrt><mn>6</mn></msqrt><mo>+</mo><msqrt><mn>14</mn></msqrt></mrow><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt><mo>+</mo><msqrt><mn>28</mn></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt><mo>.</mo><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>7</mn></msqrt><mo>.</mo><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>2</mn><msqrt><mn>7</mn></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt><mo>.</mo><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><msqrt><mn>7</mn></msqrt></mrow></mfenced></mrow><mrow><mn>2</mn><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><msqrt><mn>7</mn></msqrt></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></math></p>

Free Form

Lớp 9

$\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}$

$\begin{aligned} &\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\\ &=\frac{\sqrt{2}+\sqrt{3}+2+2+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{4}+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\\ &=\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{2}.\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\\ &=\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=1+\sqrt{2} \end{aligned}$

https://khoahoc.vietjack.com/question/1008461

### Câu hỏi: $\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}$ ### Lời giải: $\begin{aligned} &\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\\ &=\frac{\sqrt{2}+\sqrt{3}+2+2+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{4}+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\\ &=\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{2}.\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\\ &=\frac{\left(1+\sqrt{2}\right)\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=1+\sqrt{2} \end{aligned}$

Free Form

Lớp 9

<p>Tính</p> <p>$ \sqrt{3-\sqrt{29-12\sqrt{5}}}$</p>

<p>$ \begin{array}{l}\sqrt{3-\sqrt{29-12\sqrt{5}}}=\sqrt{3-\sqrt{{3}^{2}-\mathrm{2.3.2}\sqrt{5}+{\left(2\sqrt{5}\right)}^{2}}}\\ =\sqrt{3-\sqrt{{\left(2\sqrt{5}-3\right)}^{2}}}=\sqrt{3-\left(2\sqrt{5}-3\right)}=\sqrt{6-2\sqrt{5}}\\ =\sqrt{5-2\sqrt{5}.1+1}=\sqrt{{\left(\sqrt{5}-1\right)}^{2}}=\sqrt{5}-1\end{array}$</p>

https://khoahoc.vietjack.com/question/1008465

### Câu hỏi: <p>Tính</p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>29</mn><mo>−</mo><mn>12</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt></math></p> ### Lời giải: <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>29</mn><mo>−</mo><mn>12</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt><mo>=</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><msup><mn>3</mn><mn>2</mn></msup><mo>−</mo><mn>2.3.2</mn><msqrt><mn>5</mn></msqrt><mo>+</mo><msup><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt></mrow></mfenced><mn>2</mn></msup></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><msup><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup></msqrt></msqrt><mo>=</mo><msqrt><mn>3</mn><mo>−</mo><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn></mrow></mfenced></msqrt><mo>=</mo><msqrt><mn>6</mn><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>5</mn><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt><mn>.1</mn><mo>+</mo><mn>1</mn></msqrt><mo>=</mo><msqrt><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>=</mo><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mtd></mtr></mtable></math></p>

Free Form

Lớp 9

<p>Tính</p> $ \sqrt{17-4\sqrt{9+4\sqrt{5}}}$

$ \begin{array}{l}\sqrt{17-4\sqrt{9+4\sqrt{5}}}=\sqrt{17-4\sqrt{5+2\sqrt{5}.2+4}}\\ =\sqrt{17-4\sqrt{{\left(\sqrt{5}+2\right)}^{2}}}=\sqrt{17-4\left(2+\sqrt{5}\right)}\\ =\sqrt{9-4\sqrt{5}}=\sqrt{5-2\sqrt{5}.2+4}=\sqrt{{\left(\sqrt{5}-2\right)}^{2}}=\sqrt{5}-2\end{array}$

https://khoahoc.vietjack.com/question/1008467

### Câu hỏi: <p>Tính</p> <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>17</mn><mo>−</mo><mn>4</mn><msqrt><mn>9</mn><mo>+</mo><mn>4</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>17</mn><mo>−</mo><mn>4</mn><msqrt><mn>9</mn><mo>+</mo><mn>4</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt><mo>=</mo><msqrt><mn>17</mn><mo>−</mo><mn>4</mn><msqrt><mn>5</mn><mo>+</mo><mn>2</mn><msqrt><mn>5</mn></msqrt><mn>.2</mn><mo>+</mo><mn>4</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>17</mn><mo>−</mo><mn>4</mn><msqrt><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt></msqrt><mo>=</mo><msqrt><mn>17</mn><mo>−</mo><mn>4</mn><mfenced><mrow><mn>2</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>9</mn><mo>−</mo><mn>4</mn><msqrt><mn>5</mn></msqrt></msqrt><mo>=</mo><msqrt><mn>5</mn><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt><mn>.2</mn><mo>+</mo><mn>4</mn></msqrt><mo>=</mo><msqrt><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>=</mo><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>2</mn></mtd></mtr></mtable></math>

Free Form

Lớp 9

$ \sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}$

$ \begin{array}{l}\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{{\left(2\sqrt{5}\right)}^{2}-2.2\sqrt{5}.3+{3}^{2}}}}\\ =\sqrt{\sqrt{5}-\sqrt{3-\sqrt{{\left(2\sqrt{5}-3\right)}^{2}}}}=\sqrt{\sqrt{5}-\sqrt{3-\left(2\sqrt{5}-3\right)}}\\ =\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}=\sqrt{\sqrt{5}-\sqrt{{\left(\sqrt{5}-1\right)}^{2}}}=\sqrt{\sqrt{5}-\sqrt{5}+1}=\sqrt{1}=1\end{array}$

https://khoahoc.vietjack.com/question/1008471

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>29</mn><mo>−</mo><mn>12</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>29</mn><mo>−</mo><mn>12</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt></msqrt><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><msup><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt></mrow></mfenced><mn>2</mn></msup><mo>−</mo><mn>2.2</mn><msqrt><mn>5</mn></msqrt><mn>.3</mn><mo>+</mo><msup><mn>3</mn><mn>2</mn></msup></msqrt></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><msup><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup></msqrt></msqrt></msqrt><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn></mrow></mfenced></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>6</mn><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt></msqrt><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>=</mo><msqrt><mn>1</mn></msqrt><mo>=</mo><mn>1</mn></mtd></mtr></mtable></math>

Free Form

Lớp 9

<p>Tính</p> <p>$ \sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}$</p>

<p>$ \begin{array}{l}\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{{\left(2\sqrt{5}\right)}^{2}-2.2\sqrt{5}.3+{3}^{2}}}}\\ =\sqrt{\sqrt{5}-\sqrt{3-\sqrt{{\left(2\sqrt{5}-3\right)}^{2}}}}=\sqrt{\sqrt{5}-\sqrt{3-\left(2\sqrt{5}-3\right)}}\\ =\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}=\sqrt{\sqrt{5}-\sqrt{{\left(\sqrt{5}-1\right)}^{2}}}=\sqrt{\sqrt{5}-\sqrt{5}+1}=\sqrt{1}=1\end{array}$</p>

https://khoahoc.vietjack.com/question/1008472

### Câu hỏi: <p>Tính</p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>29</mn><mo>−</mo><mn>12</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt></msqrt></math></p> ### Lời giải: <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>29</mn><mo>−</mo><mn>12</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt></msqrt><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><msup><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt></mrow></mfenced><mn>2</mn></msup><mo>−</mo><mn>2.2</mn><msqrt><mn>5</mn></msqrt><mn>.3</mn><mo>+</mo><msup><mn>3</mn><mn>2</mn></msup></msqrt></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><msup><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup></msqrt></msqrt></msqrt><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn></mrow></mfenced></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>6</mn><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt></msqrt><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>=</mo><msqrt><mn>1</mn></msqrt><mo>=</mo><mn>1</mn></mtd></mtr></mtable></math></p>

Free Form

Lớp 9

$ \left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}$

$ \begin{array}{l}\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\\ =\left(4+\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)\sqrt{2}.\sqrt{4-\sqrt{15}}=\left(4+\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)\sqrt{8-2\sqrt{15}}\\ =\left(4+\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)\sqrt{{\left(\sqrt{5}-\sqrt{3}\right)}^{2}}=\left(4+\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)\\ =\left(4+\sqrt{15}\right){\left(\sqrt{5}-\sqrt{3}\right)}^{2}=\left(4+\sqrt{15}\right)\left(8-2\sqrt{15}\right)\\ =32+8\sqrt{15}-8\sqrt{15}-30=2\end{array}$

https://khoahoc.vietjack.com/question/1008476

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>4</mn><mo>+</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>10</mn></msqrt><mo>−</mo><msqrt><mn>6</mn></msqrt></mrow></mfenced><msqrt><mn>4</mn><mo>−</mo><msqrt><mn>15</mn></msqrt></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfenced><mrow><mn>4</mn><mo>+</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>10</mn></msqrt><mo>−</mo><msqrt><mn>6</mn></msqrt></mrow></mfenced><msqrt><mn>4</mn><mo>−</mo><msqrt><mn>15</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mn>4</mn><mo>+</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><msqrt><mn>2</mn></msqrt><mo>.</mo><msqrt><mn>4</mn><mo>−</mo><msqrt><mn>15</mn></msqrt></msqrt><mo>=</mo><mfenced><mrow><mn>4</mn><mo>+</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><msqrt><mn>8</mn><mo>−</mo><mn>2</mn><msqrt><mn>15</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mn>4</mn><mo>+</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><msqrt><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mn>2</mn></msup></msqrt><mo>=</mo><mfenced><mrow><mn>4</mn><mo>+</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mn>4</mn><mo>+</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mn>2</mn></msup><mo>=</mo><mfenced><mrow><mn>4</mn><mo>+</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><mfenced><mrow><mn>8</mn><mo>−</mo><mn>2</mn><msqrt><mn>15</mn></msqrt></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mn>32</mn><mo>+</mo><mn>8</mn><msqrt><mn>15</mn></msqrt><mo>−</mo><mn>8</mn><msqrt><mn>15</mn></msqrt><mo>−</mo><mn>30</mn><mo>=</mo><mn>2</mn></mtd></mtr></mtable></math>

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Lớp 9

<p>Tính</p> <div><span>$ \begin{array}{l}\text{\hspace{0.17em}}\left(3+\sqrt{5}\right)\left(\sqrt{10}-\sqrt{2}\right)\sqrt{3-\sqrt{5}}\end{array}$</span></div>

<div>$ \begin{array}{l}\left(3+\sqrt{5}\right)\left(\sqrt{10}-\sqrt{2}\right)\sqrt{3-\sqrt{5}}\\ =\left(3+\sqrt{5}\right)\left(\sqrt{5}-1\right)\sqrt{2}.\sqrt{3-\sqrt{5}}=\left(3+\sqrt{5}\right)\left(\sqrt{5}-1\right)\sqrt{6-2\sqrt{5}}\\ =\left(3+\sqrt{5}\right)\left(\sqrt{5}-1\right)\left(\sqrt{5}-1\right)=\left(3+\sqrt{5}\right){\left(\sqrt{5}-1\right)}^{2}\\ =\left(3+\sqrt{5}\right)\left(6-2\sqrt{5}\right)=18+6\sqrt{5}-6\sqrt{5}-10=8\end{array}$</div>

https://khoahoc.vietjack.com/question/1008482

### Câu hỏi: <p>Tính</p> <div><span><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mtext> </mtext><mfenced><mrow><mn>3</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>10</mn></msqrt><mo>−</mo><msqrt><mn>2</mn></msqrt></mrow></mfenced><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>5</mn></msqrt></msqrt></mtd></mtr></mtable></math></span></div> ### Lời giải: <div><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfenced><mrow><mn>3</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>10</mn></msqrt><mo>−</mo><msqrt><mn>2</mn></msqrt></mrow></mfenced><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>5</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mn>3</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><msqrt><mn>2</mn></msqrt><mo>.</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>5</mn></msqrt></msqrt><mo>=</mo><mfenced><mrow><mn>3</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><msqrt><mn>6</mn><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mn>3</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mfenced><mrow><mn>3</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mn>3</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><mn>6</mn><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></mrow></mfenced><mo>=</mo><mn>18</mn><mo>+</mo><mn>6</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>6</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>10</mn><mo>=</mo><mn>8</mn></mtd></mtr></mtable></math></div>

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Lớp 7

Cho hình vẽ sau: [https://video.vietjack.com/upload2/quiz_source1/2022/08/2-1660054613.png](https://video.vietjack.com/upload2/quiz_source1/2022/08/2-1660054613.png) Điền vào chỗ trống (…) trong các câu sau: \(\widehat {BAC}\) và \(\widehat {ACD}\) là một cặp góc …;

Hướng dẫn giải: \(\widehat {BAC}\) và \(\widehat {ACD}\) là một cặp góc **so le trong**;

https://khoahoc.vietjack.com/question/1008483

### Câu hỏi: Cho hình vẽ sau: [https://video.vietjack.com/upload2/quiz_source1/2022/08/2-1660054613.png](https://video.vietjack.com/upload2/quiz_source1/2022/08/2-1660054613.png) Điền vào chỗ trống (…) trong các câu sau: \(\widehat {BAC}\) và \(\widehat {ACD}\) là một cặp góc …; ### Lời giải: Hướng dẫn giải: \(\widehat {BAC}\) và \(\widehat {ACD}\) là một cặp góc **so le trong**;

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Lớp 7

Điền vào chỗ trống (…) trong các câu sau: \(\widehat {BAO}\) và \(\widehat {BOC}\) là một cặp góc …;

\(\widehat {BAO}\) và \(\widehat {BOC}\) là một cặp góc **<em>đồng vị</em>**;

https://khoahoc.vietjack.com/question/1008486

### Câu hỏi: Điền vào chỗ trống (…) trong các câu sau: \(\widehat {BAO}\) và \(\widehat {BOC}\) là một cặp góc …; ### Lời giải: \(\widehat {BAO}\) và \(\widehat {BOC}\) là một cặp góc **<em>đồng vị</em>**;

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Lớp 7

Điền vào chỗ trống (…) trong các câu sau: \(\widehat {DAC}\) và \(\widehat {ACB}\) là một cặp góc …;

Hướng dẫn giải: \(\widehat {DAC}\) và \(\widehat {ACB}\) là một cặp góc **so le trong**;

https://khoahoc.vietjack.com/question/1008487

### Câu hỏi: Điền vào chỗ trống (…) trong các câu sau: \(\widehat {DAC}\) và \(\widehat {ACB}\) là một cặp góc …; ### Lời giải: Hướng dẫn giải: \(\widehat {DAC}\) và \(\widehat {ACB}\) là một cặp góc **so le trong**;

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Lớp 7

Điền vào chỗ trống (…) trong các câu sau: \(\widehat {AOD}\) và \(\widehat {OCD}\) là một cặp góc ….

Hướng dẫn giải: \(\widehat {AOD}\) và \(\widehat {OCD}\) là một cặp góc **đồng vị**.

https://khoahoc.vietjack.com/question/1008489

### Câu hỏi: Điền vào chỗ trống (…) trong các câu sau: \(\widehat {AOD}\) và \(\widehat {OCD}\) là một cặp góc …. ### Lời giải: Hướng dẫn giải: \(\widehat {AOD}\) và \(\widehat {OCD}\) là một cặp góc **đồng vị**.

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Lớp 7

Thực hiện phép tính: $ \frac{-3}{16}+\frac{5}{6}$

$ \frac{-3}{16}+\frac{5}{6}=\frac{-9}{48}+\frac{40}{48}=\frac{31}{48}$

https://khoahoc.vietjack.com/question/1008507

### Câu hỏi: Thực hiện phép tính: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>−</mo><mn>3</mn></mrow><mn>16</mn></mfrac><mo>+</mo><mfrac><mn>5</mn><mn>6</mn></mfrac></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>−</mo><mn>3</mn></mrow><mn>16</mn></mfrac><mo>+</mo><mfrac><mn>5</mn><mn>6</mn></mfrac><mo>=</mo><mfrac><mrow><mo>−</mo><mn>9</mn></mrow><mn>48</mn></mfrac><mo>+</mo><mfrac><mn>40</mn><mn>48</mn></mfrac><mo>=</mo><mfrac><mn>31</mn><mn>48</mn></mfrac></math>

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Lớp 7

$ \frac{7}{20}-\frac{8}{15}$

$ \frac{7}{20}-\frac{8}{15}=\frac{21}{60}-\frac{32}{60}=\frac{-11}{60}$

https://khoahoc.vietjack.com/question/1008512

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>20</mn></mfrac><mo>−</mo><mfrac><mn>8</mn><mn>15</mn></mfrac></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>20</mn></mfrac><mo>−</mo><mfrac><mn>8</mn><mn>15</mn></mfrac><mo>=</mo><mfrac><mn>21</mn><mn>60</mn></mfrac><mo>−</mo><mfrac><mn>32</mn><mn>60</mn></mfrac><mo>=</mo><mfrac><mrow><mo>−</mo><mn>11</mn></mrow><mn>60</mn></mfrac></math>

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Lớp 7

Thực hiện phép tính $0,7 + \frac{4}{15}$

$0,7 + \frac{4}{15} = \frac{7}{10} + \frac{4}{15} = \frac{21}{30} + \frac{8}{30} = \frac{29}{30}$

https://khoahoc.vietjack.com/question/1008514

### Câu hỏi: Thực hiện phép tính $0,7 + \frac{4}{15}$ ### Lời giải: $0,7 + \frac{4}{15} = \frac{7}{10} + \frac{4}{15} = \frac{21}{30} + \frac{8}{30} = \frac{29}{30}$

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Lớp 7

$\frac{4}{7}.\frac{5}{8}\,\,-\,\,\frac{4}{7}.\frac{1}{3}$

$\frac{4}{7}.\frac{5}{8}-\frac{4}{7}.\frac{1}{3}=\frac{4}{7}.\left(\frac{5}{8}-\frac{1}{3}\right)=\frac{4}{7}.\frac{7}{24}=\frac{1}{6}$

https://khoahoc.vietjack.com/question/1008517

### Câu hỏi: $\frac{4}{7}.\frac{5}{8}\,\,-\,\,\frac{4}{7}.\frac{1}{3}$ ### Lời giải: $\frac{4}{7}.\frac{5}{8}-\frac{4}{7}.\frac{1}{3}=\frac{4}{7}.\left(\frac{5}{8}-\frac{1}{3}\right)=\frac{4}{7}.\frac{7}{24}=\frac{1}{6}$

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Lớp 7

Thực hiện phép tính $ \frac{11}{19}+\frac{19}{18}+\frac{8}{19}-\frac{1}{18}+5,2$

$ \frac{11}{19}+\frac{19}{18}+\frac{8}{19}-\frac{1}{18}+5,2=7,2$

https://khoahoc.vietjack.com/question/1008520

### Câu hỏi: Thực hiện phép tính <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>11</mn><mn>19</mn></mfrac><mo>+</mo><mfrac><mn>19</mn><mn>18</mn></mfrac><mo>+</mo><mfrac><mn>8</mn><mn>19</mn></mfrac><mo>−</mo><mfrac><mn>1</mn><mn>18</mn></mfrac><mo>+</mo><mn>5</mn><mo>,</mo><mn>2</mn></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>11</mn><mn>19</mn></mfrac><mo>+</mo><mfrac><mn>19</mn><mn>18</mn></mfrac><mo>+</mo><mfrac><mn>8</mn><mn>19</mn></mfrac><mo>−</mo><mfrac><mn>1</mn><mn>18</mn></mfrac><mo>+</mo><mn>5</mn><mo>,</mo><mn>2</mn><mo>=</mo><mn>7</mn><mo>,</mo><mn>2</mn></math>

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Lớp 7

$\frac{3}{7} \cdot \frac{16}{15} - \frac{3}{7} \cdot \frac{2}{15}$

$\frac{3}{7} \cdot \frac{16}{15} - \frac{3}{7} \cdot \frac{2}{15} = \frac{3}{7} \cdot \left( \frac{16}{15} - \frac{2}{15} \right) = \frac{2}{5}$

https://khoahoc.vietjack.com/question/1008522

### Câu hỏi: $\frac{3}{7} \cdot \frac{16}{15} - \frac{3}{7} \cdot \frac{2}{15}$ ### Lời giải: $\frac{3}{7} \cdot \frac{16}{15} - \frac{3}{7} \cdot \frac{2}{15} = \frac{3}{7} \cdot \left( \frac{16}{15} - \frac{2}{15} \right) = \frac{2}{5}$

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Lớp 7

Thực hiện phép tính $ \left(\frac{5}{12}:3\frac{2}{6}\right)+{\left(\frac{2}{3}-\frac{1}{2}\right)}^{2}$

$ \left(\frac{5}{12}:3\frac{2}{6}\right)+{\left(\frac{2}{3}-\frac{1}{2}\right)}^{2}=\left(\frac{5}{12}:3\frac{2}{6}\right)+{\left(\frac{1}{6}\right)}^{2}=\frac{1}{8}+\frac{1}{36}=\frac{11}{72}$

https://khoahoc.vietjack.com/question/1008525

### Câu hỏi: Thực hiện phép tính <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>5</mn><mn>12</mn></mfrac><mo>:</mo><mn>3</mn><mfrac><mn>2</mn><mn>6</mn></mfrac></mrow></mfenced><mo>+</mo><msup><mfenced><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced><mn>2</mn></msup></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>5</mn><mn>12</mn></mfrac><mo>:</mo><mn>3</mn><mfrac><mn>2</mn><mn>6</mn></mfrac></mrow></mfenced><mo>+</mo><msup><mfenced><mrow><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced><mn>2</mn></msup><mo>=</mo><mfenced><mrow><mfrac><mn>5</mn><mn>12</mn></mfrac><mo>:</mo><mn>3</mn><mfrac><mn>2</mn><mn>6</mn></mfrac></mrow></mfenced><mo>+</mo><msup><mfenced><mfrac><mn>1</mn><mn>6</mn></mfrac></mfenced><mn>2</mn></msup><mo>=</mo><mfrac><mn>1</mn><mn>8</mn></mfrac><mo>+</mo><mfrac><mn>1</mn><mn>36</mn></mfrac><mo>=</mo><mfrac><mn>11</mn><mn>72</mn></mfrac></math>

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Lớp 7

Thực hiện phép tính $\frac{4^2.2^3}{2^6}$

$\frac{4^2.2^3}{2^6}=\frac{2^4.2^3}{2^6}=\frac{2^7}{2^6}=2$

https://khoahoc.vietjack.com/question/1008529

### Câu hỏi: Thực hiện phép tính $\frac{4^2.2^3}{2^6}$ ### Lời giải: $\frac{4^2.2^3}{2^6}=\frac{2^4.2^3}{2^6}=\frac{2^7}{2^6}=2$

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Lớp 7

Tìm $ x$: $ \frac{1}{2}+\frac{2}{3}\cdot x=\frac{4}{5}$

$ x=\left(\frac{4}{5}-\frac{1}{2}\right):\frac{2}{3}\Rightarrow x=\frac{3}{10}.\frac{3}{2}\Rightarrow x=\frac{9}{20}$ Vậy $ x=\frac{9}{20}$

https://khoahoc.vietjack.com/question/1008535

### Câu hỏi: Tìm <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>+</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>⋅</mo><mi>x</mi><mo>=</mo><mfrac><mn>4</mn><mn>5</mn></mfrac></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mfenced><mrow><mfrac><mn>4</mn><mn>5</mn></mfrac><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced><mo>:</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>⇒</mo><mi>x</mi><mo>=</mo><mfrac><mn>3</mn><mn>10</mn></mfrac><mo>.</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>⇒</mo><mi>x</mi><mo>=</mo><mfrac><mn>9</mn><mn>20</mn></mfrac></math> Vậy <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mfrac><mn>9</mn><mn>20</mn></mfrac></math>

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Lớp 7

Tìm x: $\frac{x}{27}=\frac{-2}{3,6}$

$\frac{x}{27}=\frac{-2}{3,6}\Rightarrow x=\frac{-2.27}{3,6}\Rightarrow x=-15$ Vậy $x=-15$

https://khoahoc.vietjack.com/question/1008537

### Câu hỏi: Tìm x: $\frac{x}{27}=\frac{-2}{3,6}$ ### Lời giải: $\frac{x}{27}=\frac{-2}{3,6}\Rightarrow x=\frac{-2.27}{3,6}\Rightarrow x=-15$ Vậy $x=-15$

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Lớp 7

Tìm x: $\left| x-12 \right|-3=2014$

$\left| x-12 \right|-3=2014\Rightarrow \left| x-12 \right|=2017\Rightarrow x\–12=2017$ hoặc $x\ –12=-2017$ $\Rightarrow x=2029$ hoặc $x=-2005$ Vậy $x=2029$ hoặc $x=-2005$

https://khoahoc.vietjack.com/question/1008542

### Câu hỏi: Tìm x: $\left| x-12 \right|-3=2014$ ### Lời giải: $\left| x-12 \right|-3=2014\Rightarrow \left| x-12 \right|=2017\Rightarrow x\–12=2017$ hoặc $x\ –12=-2017$ $\Rightarrow x=2029$ hoặc $x=-2005$ Vậy $x=2029$ hoặc $x=-2005$

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Lớp 7

Tìm x: $ 3\sqrt{x}+1=40$

$ 3\sqrt{x}+1=40\Rightarrow \sqrt{x}=13\Rightarrow x=169.$ Vậy $ x=169$

https://khoahoc.vietjack.com/question/1008547

### Câu hỏi: Tìm x: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>1</mn><mo>=</mo><mn>40</mn></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>1</mn><mo>=</mo><mn>40</mn><mo>⇒</mo><msqrt><mi>x</mi></msqrt><mo>=</mo><mn>13</mn><mo>⇒</mo><mi>x</mi><mo>=</mo><mn>169.</mn></math> Vậy <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>169</mn></math>

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Lớp 7

Tìm số học sinh của mỗi lớp 7A, 7B biết rằng số học sinh lớp 7A nhiều hơn số học sinh lớp 7B là 3 em. Tỉ số học sinh của hai lớp bằng $\frac{12}{11}$.

Gọi số học sinh lớp 7A là $x$, số học sinh lớp 7B là $y$ (ĐK: $x, y, z \in \mathbb{N}^*$, học sinh). Theo đề bài ta có $\frac{x}{y} = \frac{12}{11} \Rightarrow \frac{x}{12} = \frac{y}{11} = \frac{x - y}{12 - 11} = \frac{3}{1}$ Vậy $x = 36 \Rightarrow$ Số học sinh lớp 7A là 36 học sinh Vậy $y = 33 \Rightarrow$ Số học sinh lớp 7 B là 33 học sinh

https://khoahoc.vietjack.com/question/1008551

### Câu hỏi: Tìm số học sinh của mỗi lớp 7A, 7B biết rằng số học sinh lớp 7A nhiều hơn số học sinh lớp 7B là 3 em. Tỉ số học sinh của hai lớp bằng $\frac{12}{11}$. ### Lời giải: Gọi số học sinh lớp 7A là $x$, số học sinh lớp 7B là $y$ (ĐK: $x, y, z \in \mathbb{N}^*$, học sinh). Theo đề bài ta có $\frac{x}{y} = \frac{12}{11} \Rightarrow \frac{x}{12} = \frac{y}{11} = \frac{x - y}{12 - 11} = \frac{3}{1}$ Vậy $x = 36 \Rightarrow$ Số học sinh lớp 7A là 36 học sinh Vậy $y = 33 \Rightarrow$ Số học sinh lớp 7 B là 33 học sinh

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Lớp 7

Tìm các số $x,y,z$ biết $\frac{x}{9}=\frac{y}{3}=\frac{z}{8}$ và $x-y+z=56.$

Tìm các số $x,y,z$ biết $\frac{x}{9}=\frac{y}{3}=\frac{z}{8}$ và $x-y+z=56.$ Áp dụng tính chất của dãy tỉ số bằng nhau suy ra $\frac{x}{9}=\frac{y}{3}=\frac{z}{8}=\frac{x-y+z}{9-3+8}=\frac{56}{14}=4$ Vậy $x=36; y=12; z=32$

https://khoahoc.vietjack.com/question/1008559

### Câu hỏi: Tìm các số $x,y,z$ biết $\frac{x}{9}=\frac{y}{3}=\frac{z}{8}$ và $x-y+z=56.$ ### Lời giải: Tìm các số $x,y,z$ biết $\frac{x}{9}=\frac{y}{3}=\frac{z}{8}$ và $x-y+z=56.$ Áp dụng tính chất của dãy tỉ số bằng nhau suy ra $\frac{x}{9}=\frac{y}{3}=\frac{z}{8}=\frac{x-y+z}{9-3+8}=\frac{56}{14}=4$ Vậy $x=36; y=12; z=32$

Free Form

Lớp 7

Số học sinh ba khối 6, 7, 8 tỉ lệ với các số 41; 29; 30. Biết rằng tổng số học sinh khối 6 và 7 là 140 học sinh. Tính số học sinh mỗi khối.

Gọi số học sinh ba khối 6, 7, 8 lần lượt là $x, y, z$ (ĐK: $x, y, z \in \mathbb{N}^*$, học sinh). Theo đề bài ta có; $\frac{x}{41} = \frac{y}{29} = \frac{z}{30}$ và $x + y = 140$ Áp dụng tính chất của dãy tỉ số bằng nhau suy ra $\frac{x}{41} = \frac{y}{29} = \frac{z}{30} = \frac{x + y}{41 + 29} = \frac{140}{70} = 2$ $\frac{x}{41} = 2 \Rightarrow x = 82$ (học sinh) $\frac{y}{29} = 2 \Rightarrow y = 58$ (học sinh) $\frac{z}{30} = 2 \Rightarrow z = 60$ (học sinh) Vậy số học sinh khối 6, 7, 8 lần lượt là 82, 58, 60 học sinh.

https://khoahoc.vietjack.com/question/1008564

### Câu hỏi: Số học sinh ba khối 6, 7, 8 tỉ lệ với các số 41; 29; 30. Biết rằng tổng số học sinh khối 6 và 7 là 140 học sinh. Tính số học sinh mỗi khối. ### Lời giải: Gọi số học sinh ba khối 6, 7, 8 lần lượt là $x, y, z$ (ĐK: $x, y, z \in \mathbb{N}^*$, học sinh). Theo đề bài ta có; $\frac{x}{41} = \frac{y}{29} = \frac{z}{30}$ và $x + y = 140$ Áp dụng tính chất của dãy tỉ số bằng nhau suy ra $\frac{x}{41} = \frac{y}{29} = \frac{z}{30} = \frac{x + y}{41 + 29} = \frac{140}{70} = 2$ $\frac{x}{41} = 2 \Rightarrow x = 82$ (học sinh) $\frac{y}{29} = 2 \Rightarrow y = 58$ (học sinh) $\frac{z}{30} = 2 \Rightarrow z = 60$ (học sinh) Vậy số học sinh khối 6, 7, 8 lần lượt là 82, 58, 60 học sinh.

Free Form

Lớp 7

Tính chu vi và diện tích của một mảnh vườn hình chữ nhật có chiều dài là 10,234 m và chiều rộng là 4,7 m (làm tròn kết quả đến hàng đơn vị)

Tính chu vi: $ \left(10,234+4,7\right).2=29,868\approx 30$ (m) Tính diện tích: $ 10,234.4,7=48,0998\approx 48$ (m²)

https://khoahoc.vietjack.com/question/1008573

### Câu hỏi: Tính chu vi và diện tích của một mảnh vườn hình chữ nhật có chiều dài là 10,234 m và chiều rộng là 4,7 m (làm tròn kết quả đến hàng đơn vị) ### Lời giải: Tính chu vi: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>10</mn><mo>,</mo><mn>234</mn><mo>+</mo><mn>4</mn><mo>,</mo><mn>7</mn></mrow></mfenced><mn>.2</mn><mo>=</mo><mn>29</mn><mo>,</mo><mn>868</mn><mo>≈</mo><mo> </mo><mn>30</mn></math> (m) Tính diện tích: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>,</mo><mn>234.4</mn><mo>,</mo><mn>7</mn><mo>=</mo><mn>48</mn><mo>,</mo><mn>0998</mn><mo>≈</mo><mo> </mo><mn>48</mn></math> (m²)

Free Form

Lớp 7

$S = 1 + 2 + 2^2 + 2^3 + … + 2^{50}$ và $2^{51}$

$S = 1 + 2 + 2^2 + 2^3 + … + 2^{50}$ ta có $2S = 2 + 2^2 + 2^3 + … + 2^{50} + 2^{51}$ $\Rightarrow 2S – S = 2^{51} - 1$ $\Rightarrow S = 2^{51} - 1$ $\Rightarrow S < 2^{51}$

https://khoahoc.vietjack.com/question/1008582

### Câu hỏi: $S = 1 + 2 + 2^2 + 2^3 + … + 2^{50}$ và $2^{51}$ ### Lời giải: $S = 1 + 2 + 2^2 + 2^3 + … + 2^{50}$ ta có $2S = 2 + 2^2 + 2^3 + … + 2^{50} + 2^{51}$ $\Rightarrow 2S – S = 2^{51} - 1$ $\Rightarrow S = 2^{51} - 1$ $\Rightarrow S < 2^{51}$

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Lớp 9

$ \left(x-2y\right)\sqrt{\frac{xy}{{\left(x-2y\right)}^{2}}}\left(x<2y<0\right)$

$ x<2y<0\Rightarrow x-2y<0$ $ \left(x-2y\right)\sqrt{\frac{xy}{{\left(x-2y\right)}^{2}}}=\left(x-2y\right).\frac{\sqrt{xy}}{\left|x-2y\right|}=\left(x-2y\right).\frac{\sqrt{xy}}{-\left(x-2y\right)}=-\sqrt{xy}$

https://khoahoc.vietjack.com/question/1008621

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi></mrow></mfenced><msqrt><mfrac><mrow><mi>x</mi><mi>y</mi></mrow><msup><mfenced><mrow><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi></mrow></mfenced><mn>2</mn></msup></mfrac></msqrt><mfenced><mrow><mi>x</mi><mo>&lt;</mo><mn>2</mn><mi>y</mi><mo>&lt;</mo><mn>0</mn></mrow></mfenced></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&lt;</mo><mn>2</mn><mi>y</mi><mo>&lt;</mo><mn>0</mn><mo>⇒</mo><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi><mo>&lt;</mo><mn>0</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi></mrow></mfenced><msqrt><mfrac><mrow><mi>x</mi><mi>y</mi></mrow><msup><mfenced><mrow><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi></mrow></mfenced><mn>2</mn></msup></mfrac></msqrt><mo>=</mo><mfenced><mrow><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi></mrow></mfenced><mo>.</mo><mfrac><msqrt><mi>x</mi><mi>y</mi></msqrt><mfenced close="|" open="|"><mrow><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi></mrow></mfenced></mfrac><mo>=</mo><mfenced><mrow><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi></mrow></mfenced><mo>.</mo><mfrac><msqrt><mi>x</mi><mi>y</mi></msqrt><mrow><mo>−</mo><mfenced><mrow><mi>x</mi><mo>−</mo><mn>2</mn><mi>y</mi></mrow></mfenced></mrow></mfrac><mo>=</mo><mo>−</mo><msqrt><mi>x</mi><mi>y</mi></msqrt></math>

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Lớp 9

Rút gọn các biểu thức sau : $ \left(x-y\right)\sqrt{\frac{xy}{{\left(x-y\right)}^{2}}}$

$ \begin{array}{l}\left(x-y\right)\sqrt{\frac{xy}{{\left(x-y\right)}^{2}}}=\left(x-y\right)\frac{\sqrt{xy}}{\sqrt{{\left(x-y\right)}^{2}}}\\ =\left(x-y\right).\frac{\sqrt{xy}}{\left|x-y\right|}=\left[\begin{array}{l}\sqrt{xy}(khi\text{\hspace{0.17em}}x-y>0)\\ -\sqrt{xy}\text{\hspace{0.17em}}(khi\text{\hspace{0.17em}}x-y<0)\end{array}\right.\end{array}$

https://khoahoc.vietjack.com/question/1008625

### Câu hỏi: Rút gọn các biểu thức sau : <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>x</mi><mo>−</mo><mi>y</mi></mrow></mfenced><msqrt><mfrac><mrow><mi>x</mi><mi>y</mi></mrow><msup><mfenced><mrow><mi>x</mi><mo>−</mo><mi>y</mi></mrow></mfenced><mn>2</mn></msup></mfrac></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfenced><mrow><mi>x</mi><mo>−</mo><mi>y</mi></mrow></mfenced><msqrt><mfrac><mrow><mi>x</mi><mi>y</mi></mrow><msup><mfenced><mrow><mi>x</mi><mo>−</mo><mi>y</mi></mrow></mfenced><mn>2</mn></msup></mfrac></msqrt><mo>=</mo><mfenced><mrow><mi>x</mi><mo>−</mo><mi>y</mi></mrow></mfenced><mfrac><msqrt><mi>x</mi><mi>y</mi></msqrt><msqrt><msup><mfenced><mrow><mi>x</mi><mo>−</mo><mi>y</mi></mrow></mfenced><mn>2</mn></msup></msqrt></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mi>x</mi><mo>−</mo><mi>y</mi></mrow></mfenced><mo>.</mo><mfrac><msqrt><mi>x</mi><mi>y</mi></msqrt><mfenced close="|" open="|"><mrow><mi>x</mi><mo>−</mo><mi>y</mi></mrow></mfenced></mfrac><mo>=</mo><mfenced close="" open="["><mtable columnalign="left"><mtr><mtd><msqrt><mi>x</mi><mi>y</mi></msqrt><mo>(</mo><mi>k</mi><mi>h</mi><mi>i</mi><mtext> </mtext><mi>x</mi><mo>−</mo><mi>y</mi><mo>&gt;</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mo>−</mo><msqrt><mi>x</mi><mi>y</mi></msqrt><mtext> </mtext><mo>(</mo><mi>k</mi><mi>h</mi><mi>i</mi><mtext> </mtext><mi>x</mi><mo>−</mo><mi>y</mi><mo>&lt;</mo><mn>0</mn><mo>)</mo></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></math>

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Lớp 9

$ \sqrt{\frac{2\sqrt{10}+\sqrt{30}-2\sqrt{2}-\sqrt{6}}{2\sqrt{10}-2\sqrt{2}}}:\frac{2}{\sqrt{3}-1}$

$ \begin{array}{l}\sqrt{\frac{2\sqrt{10}+\sqrt{30}-2\sqrt{2}-\sqrt{6}}{2\sqrt{10}-2\sqrt{2}}}:\frac{2}{\sqrt{3}-1}\\ =\sqrt{\frac{\sqrt{2}\left(2\sqrt{5}+\sqrt{15}-2-\sqrt{3}\right)}{\sqrt{2}\left(2\sqrt{5}-2\right)}}:\frac{2}{\sqrt{3}-1}\\ =\sqrt{\frac{\sqrt{5}\left(2+\sqrt{3}\right)-\left(2+\sqrt{3}\right)}{2\sqrt{5}-2}}.\frac{\sqrt{3}-1}{2}\\ =\sqrt{\frac{\left(2+\sqrt{3}\right)\left(\sqrt{5}-1\right)}{2\left(\sqrt{5}-1\right)}}.\frac{\sqrt{3}-1}{2}=\sqrt{\frac{2+\sqrt{3}}{2}}.\frac{\sqrt{3}-1}{2}\\ =\frac{\left(\sqrt{4+2\sqrt{3}}\right)\left(\sqrt{3}-1\right)}{2.2}=\frac{\sqrt{{\left(\sqrt{3}+1\right)}^{2}}.\left(\sqrt{3}-1\right)}{4}\\ =\frac{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)}{4}=\frac{3-1}{4}=\frac{1}{2}\end{array}$

https://khoahoc.vietjack.com/question/1008628

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>2</mn><msqrt><mn>10</mn></msqrt><mo>+</mo><msqrt><mn>30</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>2</mn></msqrt><mo>−</mo><msqrt><mn>6</mn></msqrt></mrow><mrow><mn>2</mn><msqrt><mn>10</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>2</mn></msqrt></mrow></mfrac></msqrt><mo>:</mo><mfrac><mn>2</mn><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mfrac><mrow><mn>2</mn><msqrt><mn>10</mn></msqrt><mo>+</mo><msqrt><mn>30</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>2</mn></msqrt><mo>−</mo><msqrt><mn>6</mn></msqrt></mrow><mrow><mn>2</mn><msqrt><mn>10</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>2</mn></msqrt></mrow></mfrac></msqrt><mo>:</mo><mfrac><mn>2</mn><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mfrac><mrow><msqrt><mn>2</mn></msqrt><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>+</mo><msqrt><mn>15</mn></msqrt><mo>−</mo><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced></mrow><mrow><msqrt><mn>2</mn></msqrt><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>2</mn></mrow></mfenced></mrow></mfrac></msqrt><mo>:</mo><mfrac><mn>2</mn><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mfrac><mrow><msqrt><mn>5</mn></msqrt><mfenced><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mo>−</mo><mfenced><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced></mrow><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>2</mn></mrow></mfrac></msqrt><mo>.</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mfrac><mrow><mfenced><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></mrow><mrow><mn>2</mn><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></msqrt><mo>.</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow><mn>2</mn></mfrac><mo>=</mo><msqrt><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mn>2</mn></mfrac></msqrt><mo>.</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mfenced><msqrt><mn>4</mn><mo>+</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></msqrt></mfenced><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></mrow><mn>2.2</mn></mfrac><mo>=</mo><mfrac><mrow><msqrt><msup><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>.</mo><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></mrow><mn>4</mn></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></mrow><mn>4</mn></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mo>−</mo><mn>1</mn></mrow><mn>4</mn></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mtd></mtr></mtable></math>

Free Form

Lớp 9

Đưa thừa số ra ngoài dấu căn: $ \sqrt{275}$

$ \sqrt{275}=\sqrt{25.11}=5\sqrt{11}$

https://khoahoc.vietjack.com/question/1008629

### Câu hỏi: Đưa thừa số ra ngoài dấu căn: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>275</mn></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>275</mn></msqrt><mo>=</mo><msqrt><mn>25.11</mn></msqrt><mo>=</mo><mn>5</mn><msqrt><mn>11</mn></msqrt></math>

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Lớp 9

Đưa thừa số ra ngoài dấu căn: $ 5\sqrt{70\text{\hspace{0.17em}}000}$

$ 5\sqrt{70000}=5\sqrt{10000.7}=5.100\sqrt{7}=500\sqrt{7}$

https://khoahoc.vietjack.com/question/1008630

### Câu hỏi: Đưa thừa số ra ngoài dấu căn: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><msqrt><mn>70</mn><mtext> </mtext><mn>000</mn></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><msqrt><mn>70000</mn></msqrt><mo>=</mo><mn>5</mn><msqrt><mn>10000.7</mn></msqrt><mo>=</mo><mn>5.100</mn><msqrt><mn>7</mn></msqrt><mo>=</mo><mn>500</mn><msqrt><mn>7</mn></msqrt></math>

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Lớp 9

Đưa thừa số ra ngoài dấu căn: $ \sqrt{3{x}^{2}-12x+12}$

$ \sqrt{3{x}^{2}-12x+12}=\sqrt{3.\left({x}^{2}-4x+4\right)}=\sqrt{3{\left(x-2\right)}^{2}}=\sqrt{3}.\left|x-2\right|$

https://khoahoc.vietjack.com/question/1008631

### Câu hỏi: Đưa thừa số ra ngoài dấu căn: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>12</mn><mi>x</mi><mo>+</mo><mn>12</mn></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>12</mn><mi>x</mi><mo>+</mo><mn>12</mn></msqrt><mo>=</mo><msqrt><mn>3.</mn><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced></msqrt><mo>=</mo><msqrt><mn>3</mn><msup><mfenced><mrow><mi>x</mi><mo>−</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>=</mo><msqrt><mn>3</mn></msqrt><mo>.</mo><mfenced close="|" open="|"><mrow><mi>x</mi><mo>−</mo><mn>2</mn></mrow></mfenced></math>

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Lớp 9

Đưa thừa số ra ngoài dấu căn: $ \sqrt{{x}^{4}-2{x}^{3}+3{x}^{2}-4x+2}$

$ \begin{array}{l}\sqrt{{x}^{4}-2{x}^{3}+3{x}^{2}-4x+2}=\sqrt{\left({x}^{4}-2{x}^{3}+{x}^{2}\right)+\left(2{x}^{2}-4x+2\right)}\\ =\sqrt{{x}^{2}\left({x}^{2}-2x+1\right)+2\left({x}^{2}-2x+1\right)}=\sqrt{\left({x}^{2}-2x+1\right)\left({x}^{2}+2\right)}\\ =\sqrt{{\left(x-1\right)}^{2}\left({x}^{2}+2\right)}=\left|x-1\right|\sqrt{{x}^{2}+2}\end{array}$

https://khoahoc.vietjack.com/question/1008636

### Câu hỏi: Đưa thừa số ra ngoài dấu căn: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><msup><mi>x</mi><mn>4</mn></msup><mo>−</mo><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>2</mn></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><msup><mi>x</mi><mn>4</mn></msup><mo>−</mo><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>2</mn></msqrt><mo>=</mo><msqrt><mfenced><mrow><msup><mi>x</mi><mn>4</mn></msup><mo>−</mo><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></mfenced><mo>+</mo><mfenced><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>2</mn></mrow></mfenced></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msup><mi>x</mi><mn>2</mn></msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mn>2</mn><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced></msqrt><mo>=</mo><msqrt><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn></mrow></mfenced></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msup><mfenced><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn></mrow></mfenced></msqrt><mo>=</mo><mfenced close="|" open="|"><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfenced><msqrt><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn></msqrt></mtd></mtr></mtable></math>

Free Form

Lớp 9

<p>Tính</p> <p>$ F=\sqrt{\frac{25+\sqrt{616}}{2}}-\sqrt{\frac{25-\sqrt{616}}{2}}$</p>

<p>$ \begin{array}{l}F=\sqrt{\frac{25+\sqrt{616}}{2}}-\sqrt{\frac{25-\sqrt{616}}{2}}=\frac{\sqrt{50+2\sqrt{616}}}{2}-\frac{\sqrt{50-2\sqrt{616}}}{2}\\ =\frac{\sqrt{{\left(\sqrt{28}\right)}^{2}+2.\sqrt{28}.\sqrt{22}+{\left(\sqrt{22}\right)}^{2}}-\sqrt{{\left(\sqrt{28}\right)}^{2}-2.\sqrt{28}.\sqrt{22}+{\left(\sqrt{22}\right)}^{2}}}{2}\\ =\frac{\sqrt{{\left(\sqrt{28}+\sqrt{22}\right)}^{2}}-\sqrt{{\left(\sqrt{28}-\sqrt{22}\right)}^{2}}}{2}=\frac{\sqrt{28}+\sqrt{22}-\sqrt{28}+\sqrt{22}}{2}=\sqrt{22}\end{array}$</p>

https://khoahoc.vietjack.com/question/1008640

### Câu hỏi: <p>Tính</p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><msqrt><mfrac><mrow><mn>25</mn><mo>+</mo><msqrt><mn>616</mn></msqrt></mrow><mn>2</mn></mfrac></msqrt><mo>−</mo><msqrt><mfrac><mrow><mn>25</mn><mo>−</mo><msqrt><mn>616</mn></msqrt></mrow><mn>2</mn></mfrac></msqrt></math></p> ### Lời giải: <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi>F</mi><mo>=</mo><msqrt><mfrac><mrow><mn>25</mn><mo>+</mo><msqrt><mn>616</mn></msqrt></mrow><mn>2</mn></mfrac></msqrt><mo>−</mo><msqrt><mfrac><mrow><mn>25</mn><mo>−</mo><msqrt><mn>616</mn></msqrt></mrow><mn>2</mn></mfrac></msqrt><mo>=</mo><mfrac><msqrt><mn>50</mn><mo>+</mo><mn>2</mn><msqrt><mn>616</mn></msqrt></msqrt><mn>2</mn></mfrac><mo>−</mo><mfrac><msqrt><mn>50</mn><mo>−</mo><mn>2</mn><msqrt><mn>616</mn></msqrt></msqrt><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><msup><mfenced><msqrt><mn>28</mn></msqrt></mfenced><mn>2</mn></msup><mo>+</mo><mn>2.</mn><msqrt><mn>28</mn></msqrt><mo>.</mo><msqrt><mn>22</mn></msqrt><mo>+</mo><msup><mfenced><msqrt><mn>22</mn></msqrt></mfenced><mn>2</mn></msup></msqrt><mo>−</mo><msqrt><msup><mfenced><msqrt><mn>28</mn></msqrt></mfenced><mn>2</mn></msup><mo>−</mo><mn>2.</mn><msqrt><mn>28</mn></msqrt><mo>.</mo><msqrt><mn>22</mn></msqrt><mo>+</mo><msup><mfenced><msqrt><mn>22</mn></msqrt></mfenced><mn>2</mn></msup></msqrt></mrow><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><msup><mfenced><mrow><msqrt><mn>28</mn></msqrt><mo>+</mo><msqrt><mn>22</mn></msqrt></mrow></mfenced><mn>2</mn></msup></msqrt><mo>−</mo><msqrt><msup><mfenced><mrow><msqrt><mn>28</mn></msqrt><mo>−</mo><msqrt><mn>22</mn></msqrt></mrow></mfenced><mn>2</mn></msup></msqrt></mrow><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><msqrt><mn>28</mn></msqrt><mo>+</mo><msqrt><mn>22</mn></msqrt><mo>−</mo><msqrt><mn>28</mn></msqrt><mo>+</mo><msqrt><mn>22</mn></msqrt></mrow><mn>2</mn></mfrac><mo>=</mo><msqrt><mn>22</mn></msqrt></mtd></mtr></mtable></math></p>

Free Form

Lớp 9

<div><span>Giải phương trình:</span></div> <div><span>$ \frac{2}{3}\sqrt{9x}-3\sqrt{4x}=\sqrt{25x}-16$</span></div>

<div>$ \begin{array}{l}\frac{2}{3}\sqrt{9x}-3\sqrt{4x}=\sqrt{25x}-16\left(x\ge 0\right)\\ \Leftrightarrow \frac{2}{3}.3\sqrt{x}-3.2\sqrt{x}-5\sqrt{x}=-16\\ \Leftrightarrow -9\sqrt{x}=-16\Leftrightarrow \sqrt{x}=\frac{16}{9}\\ \Rightarrow x=\frac{256}{81}\left(tm\right)\end{array}$</div>

https://khoahoc.vietjack.com/question/1008643

### Câu hỏi: <div><span>Giải phương trình:</span></div> <div><span><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mn>3</mn></mfrac><msqrt><mn>9</mn><mi>x</mi></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>4</mn><mi>x</mi></msqrt><mo>=</mo><msqrt><mn>25</mn><mi>x</mi></msqrt><mo>−</mo><mn>16</mn><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo></math></span></div> ### Lời giải: <div><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfrac><mn>2</mn><mn>3</mn></mfrac><msqrt><mn>9</mn><mi>x</mi></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>4</mn><mi>x</mi></msqrt><mo>=</mo><msqrt><mn>25</mn><mi>x</mi></msqrt><mo>−</mo><mn>16</mn><mfenced><mrow><mi>x</mi><mo>≥</mo><mn>0</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mo>⇔</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mn>.3</mn><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>3.2</mn><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>5</mn><msqrt><mi>x</mi></msqrt><mo>=</mo><mo>−</mo><mn>16</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><mo>−</mo><mn>9</mn><msqrt><mi>x</mi></msqrt><mo>=</mo><mo>−</mo><mn>16</mn><mo>⇔</mo><msqrt><mi>x</mi></msqrt><mo>=</mo><mfrac><mn>16</mn><mn>9</mn></mfrac></mtd></mtr><mtr><mtd><mo>⇒</mo><mi>x</mi><mo>=</mo><mfrac><mn>256</mn><mn>81</mn></mfrac><mo>(</mo><mi>t</mi><mi>m</mi><mo>)</mo></mtd></mtr></mtable></math></div>

Free Form

Lớp 9

Giải phương trình: $ 4\sqrt{x+5}=16$

$ \begin{array}{l}4\sqrt{x+5}=16\\ \Leftrightarrow \sqrt{x+5}=4\left(x\ge -5\right)\\ \Rightarrow x+5=16\Leftrightarrow x=11\left(tm\right)\end{array}$

https://khoahoc.vietjack.com/question/1008647

### Câu hỏi: Giải phương trình: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><msqrt><mi>x</mi><mo>+</mo><mn>5</mn></msqrt><mo>=</mo><mn>16</mn></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mn>4</mn><msqrt><mi>x</mi><mo>+</mo><mn>5</mn></msqrt><mo>=</mo><mn>16</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><msqrt><mi>x</mi><mo>+</mo><mn>5</mn></msqrt><mo>=</mo><mn>4</mn><mfenced><mrow><mi>x</mi><mo>≥</mo><mo>−</mo><mn>5</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mo>⇒</mo><mi>x</mi><mo>+</mo><mn>5</mn><mo>=</mo><mn>16</mn><mo>⇔</mo><mi>x</mi><mo>=</mo><mn>11</mn><mo>(</mo><mi>t</mi><mi>m</mi><mo>)</mo></mtd></mtr></mtable></math>

Free Form

Lớp 9

$ \sqrt{4{x}^{2}-4x+1}=1-x$

$ \begin{array}{l}\sqrt{4{x}^{2}-4x+1}=1-x\left(x\le 1\right)\\ \Leftrightarrow 4{x}^{2}-4x+1=1-2x+{x}^{2}\\ \Leftrightarrow 3{x}^{2}-2x=0\Leftrightarrow x\left(3x-2\right)=0\\ \Leftrightarrow \left[\begin{array}{l}x=0\left(tm\right)\\ x=\frac{2}{3}\left(tm\right)\end{array}\right.\end{array}\frac{}{}$

https://khoahoc.vietjack.com/question/1008650

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></msqrt><mo>=</mo><mn>1</mn><mo>−</mo><mi>x</mi></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></msqrt><mo>=</mo><mn>1</mn><mo>−</mo><mi>x</mi><mfenced><mrow><mi>x</mi><mo>≤</mo><mn>1</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>1</mn><mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>x</mi><mo>=</mo><mn>0</mn><mo>⇔</mo><mi>x</mi><mfenced><mrow><mn>3</mn><mi>x</mi><mo>−</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><mfenced close="" open="["><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mn>0</mn><mo>(</mo><mi>t</mi><mi>m</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>x</mi><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>(</mo><mi>t</mi><mi>m</mi><mo>)</mo></mtd></mtr></mtable></mfenced></mtd></mtr></mtable><mfrac><mrow></mrow><mrow></mrow></mfrac></math>

Free Form

Lớp 9

$ \sqrt{4x-12}+\frac{1}{3}\sqrt{9x-27}-4=\frac{1}{2}\sqrt{16x-48}$

$ \begin{array}{l}\sqrt{4x-12}+\frac{1}{3}\sqrt{9x-27}-4=\frac{1}{2}\sqrt{16x-48}\\ \Leftrightarrow \sqrt{4(x-3)}+\frac{1}{3}\sqrt{9\left(x-3\right)}-\frac{1}{2}\sqrt{16\left(x-3\right)}=4\\ \Leftrightarrow 2\sqrt{x-3}+\sqrt{x-3}-2\sqrt{x-3}=4\left(x\ge 3\right)\\ \Leftrightarrow \sqrt{x-3}=4\Rightarrow x-3=16\Leftrightarrow x=19\left(tm\right)\end{array}$

https://khoahoc.vietjack.com/question/1008651

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>4</mn><mi>x</mi><mo>−</mo><mn>12</mn></msqrt><mo>+</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msqrt><mn>9</mn><mi>x</mi><mo>−</mo><mn>27</mn></msqrt><mo>−</mo><mn>4</mn><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msqrt><mn>16</mn><mi>x</mi><mo>−</mo><mn>48</mn></msqrt><mo> </mo></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>4</mn><mi>x</mi><mo>−</mo><mn>12</mn></msqrt><mo>+</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msqrt><mn>9</mn><mi>x</mi><mo>−</mo><mn>27</mn></msqrt><mo>−</mo><mn>4</mn><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msqrt><mn>16</mn><mi>x</mi><mo>−</mo><mn>48</mn></msqrt></mtd></mtr><mtr><mtd><mo>⇔</mo><msqrt><mn>4</mn><mo>(</mo><mi>x</mi><mo>−</mo><mn>3</mn><mo>)</mo></msqrt><mo>+</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msqrt><mn>9</mn><mfenced><mrow><mi>x</mi><mo>−</mo><mn>3</mn></mrow></mfenced></msqrt><mo>−</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msqrt><mn>16</mn><mfenced><mrow><mi>x</mi><mo>−</mo><mn>3</mn></mrow></mfenced></msqrt><mo>=</mo><mn>4</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>2</mn><msqrt><mi>x</mi><mo>−</mo><mn>3</mn></msqrt><mo>+</mo><msqrt><mi>x</mi><mo>−</mo><mn>3</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mi>x</mi><mo>−</mo><mn>3</mn></msqrt><mo>=</mo><mn>4</mn><mfenced><mrow><mi>x</mi><mo>≥</mo><mn>3</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mo>⇔</mo><msqrt><mi>x</mi><mo>−</mo><mn>3</mn></msqrt><mo>=</mo><mn>4</mn><mo>⇒</mo><mi>x</mi><mo>−</mo><mn>3</mn><mo>=</mo><mn>16</mn><mo>⇔</mo><mi>x</mi><mo>=</mo><mn>19</mn><mo>(</mo><mi>t</mi><mi>m</mi><mo>)</mo></mtd></mtr></mtable></math>

Free Form

Lớp 9

$ \sqrt{4x+20}-3\sqrt{5+x}+\frac{4}{3}\sqrt{9x+45}=6$

$ \begin{array}{l}\sqrt{4x+20}-3\sqrt{5+x}+\frac{4}{3}\sqrt{9x+45}=6\\ \Leftrightarrow 2\sqrt{x+5}-3\sqrt{x+5}+\frac{4}{3}\mathrm{.3.}\sqrt{x+5}=6\left(x\ge -5\right)\\ \Leftrightarrow -\sqrt{x+5}+4\sqrt{x+5}=6\\ \Leftrightarrow 3\sqrt{x+5}=6\Leftrightarrow \sqrt{x+5}=2\\ \Rightarrow x+5=4\Leftrightarrow x=-1\left(tm\right)\end{array}\frac{}{}$

https://khoahoc.vietjack.com/question/1008657

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>4</mn><mi>x</mi><mo>+</mo><mn>20</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>5</mn><mo>+</mo><mi>x</mi></msqrt><mo>+</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><msqrt><mn>9</mn><mi>x</mi><mo>+</mo><mn>45</mn></msqrt><mo>=</mo><mn>6</mn></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>4</mn><mi>x</mi><mo>+</mo><mn>20</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>5</mn><mo>+</mo><mi>x</mi></msqrt><mo>+</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><msqrt><mn>9</mn><mi>x</mi><mo>+</mo><mn>45</mn></msqrt><mo>=</mo><mn>6</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>2</mn><msqrt><mi>x</mi><mo>+</mo><mn>5</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mi>x</mi><mo>+</mo><mn>5</mn></msqrt><mo>+</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mn>.3.</mn><msqrt><mi>x</mi><mo>+</mo><mn>5</mn></msqrt><mo>=</mo><mn>6</mn><mfenced><mrow><mi>x</mi><mo>≥</mo><mo>−</mo><mn>5</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mo>⇔</mo><mo>−</mo><msqrt><mi>x</mi><mo>+</mo><mn>5</mn></msqrt><mo>+</mo><mn>4</mn><msqrt><mi>x</mi><mo>+</mo><mn>5</mn></msqrt><mo>=</mo><mn>6</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>3</mn><msqrt><mi>x</mi><mo>+</mo><mn>5</mn></msqrt><mo>=</mo><mn>6</mn><mo>⇔</mo><msqrt><mi>x</mi><mo>+</mo><mn>5</mn></msqrt><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd><mo>⇒</mo><mi>x</mi><mo>+</mo><mn>5</mn><mo>=</mo><mn>4</mn><mo>⇔</mo><mi>x</mi><mo>=</mo><mo>−</mo><mn>1</mn><mo>(</mo><mi>t</mi><mi>m</mi><mo>)</mo></mtd></mtr></mtable><mfrac><mrow></mrow><mrow></mrow></mfrac></math>

Free Form

Lớp 9

<p>Rút gọn </p> <p>$ \frac{2}{2a-1}.\sqrt{5{a}^{4}\left(1-4a+4{a}^{2}\right)}$</p>

$ \begin{array}{l}\frac{2}{2a-1}\sqrt{5{a}^{4}\left(1-4a+4{a}^{2}\right)}=\frac{2}{2a-1}.\sqrt{5}.{a}^{2}.\left|1-2a\right|\\ =\left[\begin{array}{l}-2{a}^{2}\sqrt{5}(Khi\text{\hspace{0.17em}}1-2a>0)\\ 2{a}^{2}\sqrt{5}\text{\hspace{0.17em}}(khi\text{\hspace{0.17em}}1-2a<0)\end{array}\right.\end{array}$

https://khoahoc.vietjack.com/question/1008660

### Câu hỏi: <p>Rút gọn </p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><mrow><mn>2</mn><mi>a</mi><mo>−</mo><mn>1</mn></mrow></mfrac><mo>.</mo><msqrt><mn>5</mn><msup><mi>a</mi><mn>4</mn></msup><mfenced><mrow><mn>1</mn><mo>−</mo><mn>4</mn><mi>a</mi><mo>+</mo><mn>4</mn><msup><mi>a</mi><mn>2</mn></msup></mrow></mfenced></msqrt></math></p> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfrac><mn>2</mn><mrow><mn>2</mn><mi>a</mi><mo>−</mo><mn>1</mn></mrow></mfrac><msqrt><mn>5</mn><msup><mi>a</mi><mn>4</mn></msup><mfenced><mrow><mn>1</mn><mo>−</mo><mn>4</mn><mi>a</mi><mo>+</mo><mn>4</mn><msup><mi>a</mi><mn>2</mn></msup></mrow></mfenced></msqrt><mo>=</mo><mfrac><mn>2</mn><mrow><mn>2</mn><mi>a</mi><mo>−</mo><mn>1</mn></mrow></mfrac><mo>.</mo><msqrt><mn>5</mn></msqrt><mo>.</mo><msup><mi>a</mi><mn>2</mn></msup><mo>.</mo><mfenced close="|" open="|"><mrow><mn>1</mn><mo>−</mo><mn>2</mn><mi>a</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mfenced close="" open="["><mtable columnalign="left"><mtr><mtd><mo>−</mo><mn>2</mn><msup><mi>a</mi><mn>2</mn></msup><msqrt><mn>5</mn></msqrt><mo>(</mo><mi>K</mi><mi>h</mi><mi>i</mi><mtext> </mtext><mn>1</mn><mo>−</mo><mn>2</mn><mi>a</mi><mo>&gt;</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mn>2</mn><msup><mi>a</mi><mn>2</mn></msup><msqrt><mn>5</mn></msqrt><mtext> </mtext><mo>(</mo><mi>k</mi><mi>h</mi><mi>i</mi><mtext> </mtext><mn>1</mn><mo>−</mo><mn>2</mn><mi>a</mi><mo>&lt;</mo><mn>0</mn><mo>)</mo></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></math>

Free Form

Lớp 9

Rút gọn $ \left(\frac{a\sqrt{a}+b\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\right):\left(a-b\right)+\frac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}}$

$ \begin{array}{l}\left(\frac{a\sqrt{a}+b\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\right):\left(a-b\right)+\frac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}}\\ =\left[\frac{{\sqrt{a}}^{3}+{\sqrt{b}}^{3}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\right]:\left(a-b\right)+\frac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}}\\ =\left[\frac{\left(\sqrt{a}+\sqrt{b}\right)\left(a-\sqrt{ab}+b\right)}{\sqrt{a}+\sqrt{b}}-\sqrt{ab}\right].\frac{1}{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}+\frac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}}\\ =\left(a-2\sqrt{ab}+b\right).\frac{1}{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}+\frac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}}\\ ={\left(\sqrt{a}-\sqrt{b}\right)}^{2}.\frac{1}{\left(\sqrt{a}-\sqrt{b}\right)\left(\sqrt{a}+\sqrt{b}\right)}+\frac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}}=\frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}+\sqrt{b}}+\frac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}}\\ =\frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}+\sqrt{b}\text{\hspace{0.17em}}}=1\end{array}$

https://khoahoc.vietjack.com/question/1008667

### Câu hỏi: Rút gọn <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mrow><mi>a</mi><msqrt><mi>a</mi></msqrt><mo>+</mo><mi>b</mi><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac><mo>−</mo><msqrt><mi>a</mi><mi>b</mi></msqrt></mrow></mfenced><mo>:</mo><mfenced><mrow><mi>a</mi><mo>−</mo><mi>b</mi></mrow></mfenced><mo>+</mo><mfrac><mrow><mn>2</mn><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfenced><mrow><mfrac><mrow><mi>a</mi><msqrt><mi>a</mi></msqrt><mo>+</mo><mi>b</mi><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac><mo>−</mo><msqrt><mi>a</mi><mi>b</mi></msqrt></mrow></mfenced><mo>:</mo><mfenced><mrow><mi>a</mi><mo>−</mo><mi>b</mi></mrow></mfenced><mo>+</mo><mfrac><mrow><mn>2</mn><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfenced close="]" open="["><mrow><mfrac><mrow><msup><msqrt><mi>a</mi></msqrt><mn>3</mn></msup><mo>+</mo><msup><msqrt><mi>b</mi></msqrt><mn>3</mn></msup></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac><mo>−</mo><msqrt><mi>a</mi><mi>b</mi></msqrt></mrow></mfenced><mo>:</mo><mfenced><mrow><mi>a</mi><mo>−</mo><mi>b</mi></mrow></mfenced><mo>+</mo><mfrac><mrow><mn>2</mn><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfenced close="]" open="["><mrow><mfrac><mrow><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfenced><mfenced><mrow><mi>a</mi><mo>−</mo><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>+</mo><mi>b</mi></mrow></mfenced></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac><mo>−</mo><msqrt><mi>a</mi><mi>b</mi></msqrt></mrow></mfenced><mo>.</mo><mfrac><mn>1</mn><mrow><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><msqrt><mi>b</mi></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mi>a</mi><mo>−</mo><mn>2</mn><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>+</mo><mi>b</mi></mrow></mfenced><mo>.</mo><mfrac><mn>1</mn><mrow><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><msqrt><mi>b</mi></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><msup><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><msqrt><mi>b</mi></msqrt></mrow></mfenced><mn>2</mn></msup><mo>.</mo><mfrac><mn>1</mn><mrow><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><msqrt><mi>b</mi></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><msqrt><mi>b</mi></msqrt><mtext> </mtext></mrow></mfrac><mo>=</mo><mn>1</mn></mtd></mtr></mtable></math>

Free Form

Lớp 7

Cho biết $x$ và $y$ là hai đại lượng tỉ lệ thuận với nhau và khi $x=3$ thì $y=-2,7$. Tìm hệ số tỉ lệ $k$ của $y$ đối với $x$ và biểu diễn $y$ theo $x$.

$x$ và $y$ là hai đại lượng tỉ lệ thuận với nhau nên $y=kx$. $(k\neq 0)$ Khi $x=3$ thì $y=-2,7$ ta có: $-2,7=k.3\Rightarrow k=-0,9$ Vậy hệ số tỉ lệ $k$ của $y$ đối với $x$ là: $-0,9$. Biểu diễn $y$ theo $x$ là: $y=-0,9.x$

https://khoahoc.vietjack.com/question/1008671

### Câu hỏi: Cho biết $x$ và $y$ là hai đại lượng tỉ lệ thuận với nhau và khi $x=3$ thì $y=-2,7$. Tìm hệ số tỉ lệ $k$ của $y$ đối với $x$ và biểu diễn $y$ theo $x$. ### Lời giải: $x$ và $y$ là hai đại lượng tỉ lệ thuận với nhau nên $y=kx$. $(k\neq 0)$ Khi $x=3$ thì $y=-2,7$ ta có: $-2,7=k.3\Rightarrow k=-0,9$ Vậy hệ số tỉ lệ $k$ của $y$ đối với $x$ là: $-0,9$. Biểu diễn $y$ theo $x$ là: $y=-0,9.x$

Free Form

Lớp 7

Cho biết x và y là hai đại lượng tỉ lệ thuận với nhau và khi $x=3$ thì $y=-2,7$. Tính giá trị của y khi x=2 và tính giá trị của x khi y=0,9.

* Khi $x=-2$ thay vào biểu thức $y=-0,9x$ ta có: $y = -0,9.(-2)=1,8$, vậy khi $x=-2$ thì $y=1,8$ * Khi $y=0,9$ thay vào biểu thức $y=-0,9x$ ta có: $0,9=-0,9x \Rightarrow x=-1.$ Vậy khi $y=0,9$ thì $x=-1$

https://khoahoc.vietjack.com/question/1008681

### Câu hỏi: Cho biết x và y là hai đại lượng tỉ lệ thuận với nhau và khi $x=3$ thì $y=-2,7$. Tính giá trị của y khi x=2 và tính giá trị của x khi y=0,9. ### Lời giải: * Khi $x=-2$ thay vào biểu thức $y=-0,9x$ ta có: $y = -0,9.(-2)=1,8$, vậy khi $x=-2$ thì $y=1,8$ * Khi $y=0,9$ thay vào biểu thức $y=-0,9x$ ta có: $0,9=-0,9x \Rightarrow x=-1.$ Vậy khi $y=0,9$ thì $x=-1$

Free Form

Lớp 9

Rút gọn biểu thức : $ \frac{5}{12\left(2\sqrt{5}+3\sqrt{2}\right)}-\frac{5}{12\left(2\sqrt{5}-3\sqrt{2}\right)}$

$ \begin{array}{l}\frac{5}{12\left(2\sqrt{5}+3\sqrt{2}\right)}-\frac{5}{12\left(2\sqrt{5}-3\sqrt{2}\right)}\\ =\frac{5\left(2\sqrt{5}-3\sqrt{2}\right)-5\left(2\sqrt{5}+3\sqrt{2}\right)}{12\left(2\sqrt{5}+3\sqrt{2}\right)\left(2\sqrt{5}-3\sqrt{2}\right)}\\ =\frac{10\sqrt{5}-15\sqrt{2}-10\sqrt{5}-15\sqrt{2}}{12\left(20-18\right)}=\frac{-30\sqrt{2}}{24}=\frac{-5\sqrt{2}}{4}\end{array}$

https://khoahoc.vietjack.com/question/1008684

### Câu hỏi: Rút gọn biểu thức : <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mrow><mn>12</mn><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>3</mn><msqrt><mn>2</mn></msqrt></mrow></mfenced></mrow></mfrac><mo>−</mo><mfrac><mn>5</mn><mrow><mn>12</mn><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>2</mn></msqrt></mrow></mfenced></mrow></mfrac></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfrac><mn>5</mn><mrow><mn>12</mn><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>3</mn><msqrt><mn>2</mn></msqrt></mrow></mfenced></mrow></mfrac><mo>−</mo><mfrac><mn>5</mn><mrow><mn>12</mn><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>2</mn></msqrt></mrow></mfenced></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mn>5</mn><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>2</mn></msqrt></mrow></mfenced><mo>−</mo><mn>5</mn><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>3</mn><msqrt><mn>2</mn></msqrt></mrow></mfenced></mrow><mrow><mn>12</mn><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>3</mn><msqrt><mn>2</mn></msqrt></mrow></mfenced><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>2</mn></msqrt></mrow></mfenced></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mn>10</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>15</mn><msqrt><mn>2</mn></msqrt><mo>−</mo><mn>10</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>15</mn><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>12</mn><mfenced><mrow><mn>20</mn><mo>−</mo><mn>18</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>−</mo><mn>30</mn><msqrt><mn>2</mn></msqrt></mrow><mn>24</mn></mfrac><mo>=</mo><mfrac><mrow><mo>−</mo><mn>5</mn><msqrt><mn>2</mn></msqrt></mrow><mn>4</mn></mfrac></mtd></mtr></mtable></math>

Free Form

Lớp 9

$\frac{5+\sqrt{5}}{5-\sqrt{5}}+\frac{5-\sqrt{5}}{5+\sqrt{5}}$

$\begin{aligned} \frac{5+\sqrt{5}}{5-\sqrt{5}}+\frac{5-\sqrt{5}}{5+\sqrt{5}} &= \frac{\sqrt{5}.(\sqrt{5}+1)}{\sqrt{5}.(\sqrt{5}-1)}+\frac{\sqrt{5}.(\sqrt{5}-1)}{\sqrt{5}.(\sqrt{5}+1)} \\ &= \frac{\sqrt{5}+1}{\sqrt{5}-1}+\frac{\sqrt{5}-1}{\sqrt{5}+1} = \frac{(\sqrt{5}+1)^2+(\sqrt{5}-1)^2}{(\sqrt{5}-1)(\sqrt{5}+1)} \\ &= \frac{6+2\sqrt{5}+6-2\sqrt{5}}{5-1} = \frac{12}{4} = 3 \end{aligned}$

https://khoahoc.vietjack.com/question/1008687

### Câu hỏi: $\frac{5+\sqrt{5}}{5-\sqrt{5}}+\frac{5-\sqrt{5}}{5+\sqrt{5}}$ ### Lời giải: $\begin{aligned} \frac{5+\sqrt{5}}{5-\sqrt{5}}+\frac{5-\sqrt{5}}{5+\sqrt{5}} &= \frac{\sqrt{5}.(\sqrt{5}+1)}{\sqrt{5}.(\sqrt{5}-1)}+\frac{\sqrt{5}.(\sqrt{5}-1)}{\sqrt{5}.(\sqrt{5}+1)} \\ &= \frac{\sqrt{5}+1}{\sqrt{5}-1}+\frac{\sqrt{5}-1}{\sqrt{5}+1} = \frac{(\sqrt{5}+1)^2+(\sqrt{5}-1)^2}{(\sqrt{5}-1)(\sqrt{5}+1)} \\ &= \frac{6+2\sqrt{5}+6-2\sqrt{5}}{5-1} = \frac{12}{4} = 3 \end{aligned}$

Free Form

Lớp 9

$ \frac{\sqrt{3}}{\sqrt{\sqrt{3}+1}-1}-\frac{\sqrt{3}}{\sqrt{\sqrt{3}+1}+1}$

$ \begin{array}{l}\frac{\sqrt{3}}{\sqrt{\sqrt{3}+1}-1}-\frac{\sqrt{3}}{\sqrt{\sqrt{3}+1}+1}\\ =\frac{\sqrt{3}.\left(\sqrt{\sqrt{3}+1}+1\right)-\sqrt{3}\left(\sqrt{\sqrt{3}+1}-1\right)}{\sqrt{{\left(\sqrt{3}+1\right)}^{2}}-1}\\ =\frac{\sqrt{3}.\left[\sqrt{\sqrt{3}+1}+1-\sqrt{\sqrt{3}+1}+1\right]}{\sqrt{3}+1-1}\\ =\sqrt{\sqrt{3}+1}+1-\sqrt{\sqrt{3}+1}+1=2\end{array}$

https://khoahoc.vietjack.com/question/1008713

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>3</mn></msqrt><mrow><msqrt><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac><mo>−</mo><mfrac><msqrt><mn>3</mn></msqrt><mrow><msqrt><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfrac></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfrac><msqrt><mn>3</mn></msqrt><mrow><msqrt><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac><mo>−</mo><mfrac><msqrt><mn>3</mn></msqrt><mrow><msqrt><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt><mo>.</mo><mfenced><mrow><msqrt><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced><mo>−</mo><msqrt><mn>3</mn></msqrt><mfenced><mrow><msqrt><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></mrow><mrow><msqrt><msup><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt><mo>.</mo><mfenced close="]" open="["><mrow><msqrt><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>+</mo><mn>1</mn><mo>−</mo><msqrt><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn><mo>−</mo><mn>1</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>+</mo><mn>1</mn><mo>−</mo><msqrt><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>+</mo><mn>1</mn><mo>=</mo><mn>2</mn></mtd></mtr></mtable></math>

Free Form

Lớp 9

$ \sqrt{\frac{16{x}^{3}}{81y}}$

$ \sqrt{\frac{16{x}^{3}}{81y}}=\sqrt{\frac{16}{81}}.\frac{\sqrt{{x}^{3}}}{\sqrt{y}}=\frac{4x\sqrt{x}}{9\sqrt{y}}=\frac{4x\sqrt{xy}}{9y}$

https://khoahoc.vietjack.com/question/1008891

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>16</mn><msup><mi>x</mi><mn>3</mn></msup></mrow><mrow><mn>81</mn><mi>y</mi></mrow></mfrac></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>16</mn><msup><mi>x</mi><mn>3</mn></msup></mrow><mrow><mn>81</mn><mi>y</mi></mrow></mfrac></msqrt><mo>=</mo><msqrt><mfrac><mn>16</mn><mn>81</mn></mfrac></msqrt><mo>.</mo><mfrac><msqrt><msup><mi>x</mi><mn>3</mn></msup></msqrt><msqrt><mi>y</mi></msqrt></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn><mi>x</mi><msqrt><mi>x</mi></msqrt></mrow><mrow><mn>9</mn><msqrt><mi>y</mi></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn><mi>x</mi><msqrt><mi>x</mi><mi>y</mi></msqrt></mrow><mrow><mn>9</mn><mi>y</mi></mrow></mfrac></math>

Free Form

Lớp 9

$ \sqrt{\frac{16{x}^{3}}{81y}}$

$ \sqrt{\frac{16{x}^{3}}{81y}}=\sqrt{\frac{16}{81}}.\frac{\sqrt{{x}^{3}}}{\sqrt{y}}=\frac{4x\sqrt{x}}{9\sqrt{y}}=\frac{4x\sqrt{xy}}{9y}$

https://khoahoc.vietjack.com/question/1008892

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>16</mn><msup><mi>x</mi><mn>3</mn></msup></mrow><mrow><mn>81</mn><mi>y</mi></mrow></mfrac></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>16</mn><msup><mi>x</mi><mn>3</mn></msup></mrow><mrow><mn>81</mn><mi>y</mi></mrow></mfrac></msqrt><mo>=</mo><msqrt><mfrac><mn>16</mn><mn>81</mn></mfrac></msqrt><mo>.</mo><mfrac><msqrt><msup><mi>x</mi><mn>3</mn></msup></msqrt><msqrt><mi>y</mi></msqrt></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn><mi>x</mi><msqrt><mi>x</mi></msqrt></mrow><mrow><mn>9</mn><msqrt><mi>y</mi></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>4</mn><mi>x</mi><msqrt><mi>x</mi><mi>y</mi></msqrt></mrow><mrow><mn>9</mn><mi>y</mi></mrow></mfrac></math>

Free Form

Lớp 9

$\frac{15}{\sqrt{7}-2}$

$\begin{aligned} \frac{15}{\sqrt{7}-2} &= \frac{15(\sqrt{7}+2)}{7-4} = \frac{15(\sqrt{7}+2)}{3} = 5(\sqrt{7}+2) \\ &= 5\sqrt{7}+10 \end{aligned}$

https://khoahoc.vietjack.com/question/1008899

### Câu hỏi: $\frac{15}{\sqrt{7}-2}$ ### Lời giải: $\begin{aligned} \frac{15}{\sqrt{7}-2} &= \frac{15(\sqrt{7}+2)}{7-4} = \frac{15(\sqrt{7}+2)}{3} = 5(\sqrt{7}+2) \\ &= 5\sqrt{7}+10 \end{aligned}$

Free Form

Lớp 9

$ \frac{3\sqrt{3}+3}{2\sqrt{3}}$

$ \frac{3\sqrt{3}+3}{2\sqrt{3}}=\frac{\sqrt{3}.\left(3+\sqrt{3}\right)}{2\sqrt{3}}=\frac{3+\sqrt{3}}{2}$

https://khoahoc.vietjack.com/question/1008902

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>3</mn></mrow><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt></mrow></mfrac></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>3</mn><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>3</mn></mrow><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt><mo>.</mo><mfenced><mrow><mn>3</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced></mrow><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mn>2</mn></mfrac></math>

Free Form

Lớp 9

Trục căn thức ở mẫu: $ \frac{2\sqrt{3}-\sqrt{6}}{\sqrt{2}-1}$

$ \frac{2\sqrt{3}-\sqrt{6}}{\sqrt{2}-1}=\frac{\sqrt{6}.\left(\sqrt{2}-1\right)}{\sqrt{2}-1}=\sqrt{6}$

https://khoahoc.vietjack.com/question/1008904

### Câu hỏi: Trục căn thức ở mẫu: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><msqrt><mn>6</mn></msqrt></mrow><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><msqrt><mn>6</mn></msqrt></mrow><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><msqrt><mn>6</mn></msqrt><mo>.</mo><mfenced><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></mrow><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac><mo>=</mo><msqrt><mn>6</mn></msqrt></math>

Free Form

Lớp 9

$ B=\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\mathrm{........}+\frac{1}{\sqrt{2005}+\sqrt{2006}}$

$ \begin{array}{l}B=\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\mathrm{.....}+\frac{1}{\sqrt{2004}+\sqrt{2005}}\\ =\frac{\sqrt{2}-1}{2-1}+\frac{\sqrt{3}-\sqrt{2}}{3-2}+\frac{\sqrt{4}-\sqrt{3}}{4-3}+\mathrm{......}+\frac{\sqrt{2006}-\sqrt{2005}}{2006-2005}\\ =\sqrt{2}-1+\sqrt{3}-\sqrt{2}+\sqrt{4}-\sqrt{3}+\mathrm{...}+\sqrt{2006}-\sqrt{2005}\\ =\sqrt{2006}-1\\ \end{array}$

https://khoahoc.vietjack.com/question/1008910

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>+</mo><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac><mo>+</mo><mn>........</mn><mo>+</mo><mfrac><mn>1</mn><mrow><msqrt><mn>2005</mn></msqrt><mo>+</mo><msqrt><mn>2006</mn></msqrt></mrow></mfrac></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi>B</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>+</mo><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><msqrt><mn>4</mn></msqrt></mrow></mfrac><mo>+</mo><mn>.....</mn><mo>+</mo><mfrac><mn>1</mn><mrow><msqrt><mn>2004</mn></msqrt><mo>+</mo><msqrt><mn>2005</mn></msqrt></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><mn>1</mn></mrow><mrow><mn>2</mn><mo>−</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>3</mn><mo>−</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><msqrt><mn>4</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>4</mn><mo>−</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mn>......</mn><mo>+</mo><mfrac><mrow><msqrt><mn>2006</mn></msqrt><mo>−</mo><msqrt><mn>2005</mn></msqrt></mrow><mrow><mn>2006</mn><mo>−</mo><mn>2005</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>2</mn></msqrt><mo>−</mo><mn>1</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>−</mo><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>4</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>...</mn><mo>+</mo><msqrt><mn>2006</mn></msqrt><mo>−</mo><msqrt><mn>2005</mn></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>2006</mn></msqrt><mo>−</mo><mn>1</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></math>

Free Form

Lớp 9

$ C=\frac{1}{\sqrt{1}-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-\mathrm{........}-\frac{1}{\sqrt{48}-\sqrt{49}}$

$ \begin{array}{l}C=\frac{1}{\sqrt{1}-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-\mathrm{.......}-\frac{1}{\sqrt{48}-\sqrt{49}}\\ =\frac{\sqrt{1}+\sqrt{2}}{1-2}-\frac{\sqrt{2}+\sqrt{3}}{2-3}+\frac{\sqrt{3}-\sqrt{4}}{3-4}-\mathrm{.....}-\frac{\sqrt{48}+\sqrt{49}}{48-49}\\ =-1-\sqrt{2}+\sqrt{2}+\sqrt{3}-\sqrt{3}-\sqrt{4}-\mathrm{.....}+\sqrt{48}+\sqrt{49}\\ =-1+\sqrt{49}=-1+7=6\end{array}$

https://khoahoc.vietjack.com/question/1008911

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfrac><mn>1</mn><mrow><msqrt><mn>1</mn></msqrt><mo>−</mo><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo>−</mo><mfrac><mn>1</mn><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><msqrt><mn>4</mn></msqrt></mrow></mfrac><mo>−</mo><mn>........</mn><mo>−</mo><mfrac><mn>1</mn><mrow><msqrt><mn>48</mn></msqrt><mo>−</mo><msqrt><mn>49</mn></msqrt></mrow></mfrac></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi>C</mi><mo>=</mo><mfrac><mn>1</mn><mrow><msqrt><mn>1</mn></msqrt><mo>−</mo><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo>−</mo><mfrac><mn>1</mn><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><msqrt><mn>4</mn></msqrt></mrow></mfrac><mo>−</mo><mn>.......</mn><mo>−</mo><mfrac><mn>1</mn><mrow><msqrt><mn>48</mn></msqrt><mo>−</mo><msqrt><mn>49</mn></msqrt></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><mn>1</mn></msqrt><mo>+</mo><msqrt><mn>2</mn></msqrt></mrow><mrow><mn>1</mn><mo>−</mo><mn>2</mn></mrow></mfrac><mo>−</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn><mo>−</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><msqrt><mn>4</mn></msqrt></mrow><mrow><mn>3</mn><mo>−</mo><mn>4</mn></mrow></mfrac><mo>−</mo><mn>.....</mn><mo>−</mo><mfrac><mrow><msqrt><mn>48</mn></msqrt><mo>+</mo><msqrt><mn>49</mn></msqrt></mrow><mrow><mn>48</mn><mo>−</mo><mn>49</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mo>−</mo><mn>1</mn><mo>−</mo><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt><mo>−</mo><msqrt><mn>4</mn></msqrt><mo>−</mo><mn>.....</mn><mo>+</mo><msqrt><mn>48</mn></msqrt><mo>+</mo><msqrt><mn>49</mn></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mo>−</mo><mn>1</mn><mo>+</mo><msqrt><mn>49</mn></msqrt><mo>=</mo><mo>−</mo><mn>1</mn><mo>+</mo><mn>7</mn><mo>=</mo><mn>6</mn></mtd></mtr></mtable></math>

Free Form

Lớp 9

$ D=\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\mathrm{......}+\frac{1}{100\sqrt{99}+99\sqrt{100}}$

<p> $ \begin{array}{l}\frac{1}{\left(n+1\right)\sqrt{n}+n\sqrt{n+1}}=\frac{1}{\sqrt{n\left(n+1\right)}\left(\sqrt{n+1}+\sqrt{n}\right)}\\ =\frac{\sqrt{n+1}-\sqrt{n}}{\sqrt{n\left(n+1\right)}.\left(\sqrt{n+1}+\sqrt{n}\right)}=\frac{\sqrt{n+1}-\sqrt{n}}{\sqrt{n\left(n+1\right)}}=\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n}+1}\end{array}$ </p> <p> $ D=\frac{1}{\sqrt{1}}-\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}+\mathrm{.....}+\frac{1}{\sqrt{99}}-\frac{1}{\sqrt{100}}=\frac{1}{\sqrt{1}}-\frac{1}{\sqrt{100}}=\frac{9}{10}$ </p>

https://khoahoc.vietjack.com/question/1008917

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><msqrt><mn>1</mn></msqrt><mo>+</mo><mn>1</mn><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>3</mn><msqrt><mn>2</mn></msqrt><mo>+</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></mrow></mfrac><mo>+</mo><mn>......</mn><mo>+</mo><mfrac><mn>1</mn><mrow><mn>100</mn><msqrt><mn>99</mn></msqrt><mo>+</mo><mn>99</mn><msqrt><mn>100</mn></msqrt></mrow></mfrac></math> ### Lời giải: <p> <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfrac><mn>1</mn><mrow><mfenced><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfenced><msqrt><mi>n</mi></msqrt><mo>+</mo><mi>n</mi><msqrt><mi>n</mi><mo>+</mo><mn>1</mn></msqrt></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><msqrt><mi>n</mi><mfenced><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfenced></msqrt><mfenced><mrow><msqrt><mi>n</mi><mo>+</mo><mn>1</mn></msqrt><mo>+</mo><msqrt><mi>n</mi></msqrt></mrow></mfenced></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><mi>n</mi><mo>+</mo><mn>1</mn></msqrt><mo>−</mo><msqrt><mi>n</mi></msqrt></mrow><mrow><msqrt><mi>n</mi><mfenced><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfenced></msqrt><mo>.</mo><mfenced><mrow><msqrt><mi>n</mi><mo>+</mo><mn>1</mn></msqrt><mo>+</mo><msqrt><mi>n</mi></msqrt></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><msqrt><mi>n</mi><mo>+</mo><mn>1</mn></msqrt><mo>−</mo><msqrt><mi>n</mi></msqrt></mrow><msqrt><mi>n</mi><mfenced><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfenced></msqrt></mfrac><mo>=</mo><mfrac><mn>1</mn><msqrt><mi>n</mi></msqrt></mfrac><mo>−</mo><mfrac><mn>1</mn><mrow><msqrt><mi>n</mi></msqrt><mo>+</mo><mn>1</mn></mrow></mfrac></mtd></mtr></mtable></math> </p> <p> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mfrac><mn>1</mn><msqrt><mn>1</mn></msqrt></mfrac><mo>−</mo><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac><mo>+</mo><mfrac><mn>1</mn><msqrt><mn>2</mn></msqrt></mfrac><mo>−</mo><mfrac><mn>1</mn><msqrt><mn>3</mn></msqrt></mfrac><mo>+</mo><mn>.....</mn><mo>+</mo><mfrac><mn>1</mn><msqrt><mn>99</mn></msqrt></mfrac><mo>−</mo><mfrac><mn>1</mn><msqrt><mn>100</mn></msqrt></mfrac><mo>=</mo><mfrac><mn>1</mn><msqrt><mn>1</mn></msqrt></mfrac><mo>−</mo><mfrac><mn>1</mn><msqrt><mn>100</mn></msqrt></mfrac><mo>=</mo><mfrac><mn>9</mn><mn>10</mn></mfrac></math> </p>

Free Form

Lớp 9

Rút gọn biểu thức: $ \frac{x\sqrt{x}-y\sqrt{y}}{\sqrt{x}-\sqrt{y}}$

$ \frac{x\sqrt{x}-y\sqrt{y}}{\sqrt{x}-\sqrt{y}}=\frac{{\sqrt{x}}^{3}-{\sqrt{y}}^{3}}{\sqrt{x}-\sqrt{y}}=\frac{\left(\sqrt{x}-\sqrt{y}\right)\left(x+\sqrt{xy}+y\right)}{\sqrt{x}-\sqrt{y}}=x+\sqrt{xy}+y$

https://khoahoc.vietjack.com/question/1008921

### Câu hỏi: Rút gọn biểu thức: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><msqrt><mi>x</mi></msqrt><mo>−</mo><mi>y</mi><msqrt><mi>y</mi></msqrt></mrow><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><msqrt><mi>y</mi></msqrt></mrow></mfrac></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><msqrt><mi>x</mi></msqrt><mo>−</mo><mi>y</mi><msqrt><mi>y</mi></msqrt></mrow><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><msqrt><mi>y</mi></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><msup><msqrt><mi>x</mi></msqrt><mn>3</mn></msup><mo>−</mo><msup><msqrt><mi>y</mi></msqrt><mn>3</mn></msup></mrow><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><msqrt><mi>y</mi></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><mfenced><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><msqrt><mi>y</mi></msqrt></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><msqrt><mi>x</mi><mi>y</mi></msqrt><mo>+</mo><mi>y</mi></mrow></mfenced></mrow><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><msqrt><mi>y</mi></msqrt></mrow></mfrac><mo>=</mo><mi>x</mi><mo>+</mo><msqrt><mi>x</mi><mi>y</mi></msqrt><mo>+</mo><mi>y</mi></math>

Free Form

Lớp 9

Rút gọn biểu thức: $$\frac{x-\sqrt{3x}+3}{x\sqrt{x}+3\sqrt{3}}$$

$$\begin{aligned} &\frac{x-\sqrt{3x}+3}{x\sqrt{x}+3\sqrt{3}}=\frac{x-\sqrt{3x}+3}{(\sqrt{x}+\sqrt{3})(x-\sqrt{3x}+3)}=\frac{1}{\sqrt{x}+\sqrt{3}}=\frac{x-\sqrt{3}}{x-3} \end{aligned}$$

https://khoahoc.vietjack.com/question/1008926

### Câu hỏi: Rút gọn biểu thức: $$\frac{x-\sqrt{3x}+3}{x\sqrt{x}+3\sqrt{3}}$$ ### Lời giải: $$\begin{aligned} &\frac{x-\sqrt{3x}+3}{x\sqrt{x}+3\sqrt{3}}=\frac{x-\sqrt{3x}+3}{(\sqrt{x}+\sqrt{3})(x-\sqrt{3x}+3)}=\frac{1}{\sqrt{x}+\sqrt{3}}=\frac{x-\sqrt{3}}{x-3} \end{aligned}$$

Free Form

Lớp 9

$ \sqrt{10+\sqrt{3}x}=2+\sqrt{6}$

$ \begin{array}{l}\sqrt{10+\sqrt{3x}}=2+\sqrt{6}\left(x\ge 0\right)\\ \Rightarrow 10+\sqrt{3x}=10+4\sqrt{6}\\ \sqrt{3x}=4\sqrt{6}\Rightarrow 3x=96\Leftrightarrow x=32\left(tm\right)\end{array}$

https://khoahoc.vietjack.com/question/1008931

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>10</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mi>x</mi></msqrt><mo>=</mo><mn>2</mn><mo>+</mo><msqrt><mn>6</mn></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>10</mn><mo>+</mo><msqrt><mn>3</mn><mi>x</mi></msqrt></msqrt><mo>=</mo><mn>2</mn><mo>+</mo><msqrt><mn>6</mn></msqrt><mfenced><mrow><mi>x</mi><mo>≥</mo><mn>0</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mo>⇒</mo><mn>10</mn><mo>+</mo><msqrt><mn>3</mn><mi>x</mi></msqrt><mo>=</mo><mn>10</mn><mo>+</mo><mn>4</mn><msqrt><mn>6</mn></msqrt></mtd></mtr><mtr><mtd><msqrt><mn>3</mn><mi>x</mi></msqrt><mo>=</mo><mn>4</mn><msqrt><mn>6</mn></msqrt><mo>⇒</mo><mn>3</mn><mi>x</mi><mo>=</mo><mn>96</mn><mo>⇔</mo><mi>x</mi><mo>=</mo><mn>32</mn><mo>(</mo><mi>t</mi><mi>m</mi><mo>)</mo></mtd></mtr></mtable></math>

Free Form

Lớp 9

Tìm x biết: $\sqrt{3x-2}=2-\sqrt{3}$

$\begin{aligned} \sqrt{3x-2}&=2-\sqrt{3} \left(x\geq \frac{2}{3}\right)\\ \Rightarrow 3x-2&=7-4\sqrt{3}\\ \Leftrightarrow 3x&=9-4\sqrt{3}\Rightarrow x=3-\frac{4}{3}\sqrt{3} \left(tm\right) \end{aligned}$

https://khoahoc.vietjack.com/question/1008932

### Câu hỏi: Tìm x biết: $\sqrt{3x-2}=2-\sqrt{3}$ ### Lời giải: $\begin{aligned} \sqrt{3x-2}&=2-\sqrt{3} \left(x\geq \frac{2}{3}\right)\\ \Rightarrow 3x-2&=7-4\sqrt{3}\\ \Leftrightarrow 3x&=9-4\sqrt{3}\Rightarrow x=3-\frac{4}{3}\sqrt{3} \left(tm\right) \end{aligned}$

Free Form

Lớp 9

Tìm x biết: $\sqrt{x+1}=\sqrt{5}-3$

$\begin{aligned} &\sqrt{x+1}=\sqrt{5}-3(x\geq -1)\\ &\Rightarrow x+1=14-6\sqrt{5}\\ &\Rightarrow x=13-6\sqrt{5}(tm) \end{aligned}$

https://khoahoc.vietjack.com/question/1008935

### Câu hỏi: Tìm x biết: $\sqrt{x+1}=\sqrt{5}-3$ ### Lời giải: $\begin{aligned} &\sqrt{x+1}=\sqrt{5}-3(x\geq -1)\\ &\Rightarrow x+1=14-6\sqrt{5}\\ &\Rightarrow x=13-6\sqrt{5}(tm) \end{aligned}$

Free Form

Lớp 9

$\frac{2}{\sqrt{6}-2}-\frac{4}{3-\sqrt{5}}$

$\frac{2}{\sqrt{6}-2}-\frac{4}{3-\sqrt{5}}=\frac{2(\sqrt{6}+2)}{6-4}-\frac{4(3+\sqrt{5})}{9-5}=\sqrt{6}+2-3-\sqrt{5}=\sqrt{6}-\sqrt{5}-1$

https://khoahoc.vietjack.com/question/1008955

### Câu hỏi: $\frac{2}{\sqrt{6}-2}-\frac{4}{3-\sqrt{5}}$ ### Lời giải: $\frac{2}{\sqrt{6}-2}-\frac{4}{3-\sqrt{5}}=\frac{2(\sqrt{6}+2)}{6-4}-\frac{4(3+\sqrt{5})}{9-5}=\sqrt{6}+2-3-\sqrt{5}=\sqrt{6}-\sqrt{5}-1$

Free Form

Lớp 9

$ \sqrt{96}-6\sqrt{\frac{2}{3}}+\frac{3}{3+\sqrt{6}}-\sqrt{10-4\sqrt{6}}$

$ \begin{array}{l}\sqrt{96}-6\sqrt{\frac{2}{3}}+\frac{3}{3+\sqrt{6}}-\sqrt{10-4\sqrt{6}}\\ =\sqrt{16.6}-\frac{6\sqrt{2}}{\sqrt{3}}+\frac{3\left(3-\sqrt{6}\right)}{9-6}-\sqrt{{\left(\sqrt{6}\right)}^{2}-2.\sqrt{6}.2+{2}^{2}}\\ =4\sqrt{6}-2\sqrt{6}+3-\sqrt{6}-\sqrt{{\left(\sqrt{6}-2\right)}^{2}}\\ =\sqrt{6}+3-\left|\sqrt{6}-2\right|=\sqrt{6}+3-\sqrt{6}+2=5\end{array}$

https://khoahoc.vietjack.com/question/1008959

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>96</mn></msqrt><mo>−</mo><mn>6</mn><msqrt><mfrac><mn>2</mn><mn>3</mn></mfrac></msqrt><mo>+</mo><mfrac><mn>3</mn><mrow><mn>3</mn><mo>+</mo><msqrt><mn>6</mn></msqrt></mrow></mfrac><mo>−</mo><msqrt><mn>10</mn><mo>−</mo><mn>4</mn><msqrt><mn>6</mn></msqrt></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>96</mn></msqrt><mo>−</mo><mn>6</mn><msqrt><mfrac><mn>2</mn><mn>3</mn></mfrac></msqrt><mo>+</mo><mfrac><mn>3</mn><mrow><mn>3</mn><mo>+</mo><msqrt><mn>6</mn></msqrt></mrow></mfrac><mo>−</mo><msqrt><mn>10</mn><mo>−</mo><mn>4</mn><msqrt><mn>6</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>16.6</mn></msqrt><mo>−</mo><mfrac><mrow><mn>6</mn><msqrt><mn>2</mn></msqrt></mrow><msqrt><mn>3</mn></msqrt></mfrac><mo>+</mo><mfrac><mrow><mn>3</mn><mfenced><mrow><mn>3</mn><mo>−</mo><msqrt><mn>6</mn></msqrt></mrow></mfenced></mrow><mrow><mn>9</mn><mo>−</mo><mn>6</mn></mrow></mfrac><mo>−</mo><msqrt><msup><mfenced><msqrt><mn>6</mn></msqrt></mfenced><mn>2</mn></msup><mo>−</mo><mn>2.</mn><msqrt><mn>6</mn></msqrt><mn>.2</mn><mo>+</mo><msup><mn>2</mn><mn>2</mn></msup></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mn>4</mn><msqrt><mn>6</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>6</mn></msqrt><mo>+</mo><mn>3</mn><mo>−</mo><msqrt><mn>6</mn></msqrt><mo>−</mo><msqrt><msup><mfenced><mrow><msqrt><mn>6</mn></msqrt><mo>−</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>6</mn></msqrt><mo>+</mo><mn>3</mn><mo>−</mo><mfenced close="|" open="|"><mrow><msqrt><mn>6</mn></msqrt><mo>−</mo><mn>2</mn></mrow></mfenced><mo>=</mo><msqrt><mn>6</mn></msqrt><mo>+</mo><mn>3</mn><mo>−</mo><msqrt><mn>6</mn></msqrt><mo>+</mo><mn>2</mn><mo>=</mo><mn>5</mn></mtd></mtr></mtable></math>

Free Form

Lớp 9

$ \sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}$

$ \begin{array}{l}\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}\\ =\frac{\sqrt{4+2\sqrt{3}}}{\sqrt{2}}+\frac{\sqrt{4-2\sqrt{3}}}{\sqrt{2}}=\frac{\sqrt{{\left(\sqrt{3}+1\right)}^{2}}}{\sqrt{2}}+\frac{\sqrt{{\left(\sqrt{3}-1\right)}^{2}}}{\sqrt{2}}\\ =\frac{\sqrt{3}+1+\sqrt{3}-1}{\sqrt{2}}=\frac{2\sqrt{3}}{\sqrt{2}}=\sqrt{6}\end{array}$

https://khoahoc.vietjack.com/question/1008966

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></msqrt><mo>+</mo><msqrt><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></msqrt><mo>+</mo><msqrt><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><msqrt><mn>4</mn><mo>+</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></msqrt><msqrt><mn>2</mn></msqrt></mfrac><mo>+</mo><mfrac><msqrt><mn>4</mn><mo>−</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></msqrt><msqrt><mn>2</mn></msqrt></mfrac><mo>=</mo><mfrac><msqrt><msup><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt><msqrt><mn>2</mn></msqrt></mfrac><mo>+</mo><mfrac><msqrt><msup><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt><msqrt><mn>2</mn></msqrt></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow><msqrt><mn>2</mn></msqrt></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt></mrow><msqrt><mn>2</mn></msqrt></mfrac><mo>=</mo><msqrt><mn>6</mn></msqrt></mtd></mtr></mtable></math>

Free Form

Lớp 9

Rút gọn các căn thức sau: $ \text{\hspace{0.17em}}\sqrt{\frac{1}{2}}+\sqrt{4,5}+\sqrt{12,5}$

$ \begin{array}{l}\sqrt{\frac{1}{2}}+\sqrt{4,5}+\sqrt{12,5}=\sqrt{\frac{1}{2}}+\sqrt{\frac{9}{2}}+\sqrt{\frac{25}{2}}\\ =\frac{\sqrt{2}+3\sqrt{2}+5\sqrt{2}}{2}=\frac{9\sqrt{2}}{2}\end{array}$

https://khoahoc.vietjack.com/question/1008971

### Câu hỏi: Rút gọn các căn thức sau: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext> </mtext><msqrt><mfrac><mn>1</mn><mn>2</mn></mfrac></msqrt><mo>+</mo><msqrt><mn>4</mn><mo>,</mo><mn>5</mn></msqrt><mo>+</mo><msqrt><mn>12</mn><mo>,</mo><mn>5</mn></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mfrac><mn>1</mn><mn>2</mn></mfrac></msqrt><mo>+</mo><msqrt><mn>4</mn><mo>,</mo><mn>5</mn></msqrt><mo>+</mo><msqrt><mn>12</mn><mo>,</mo><mn>5</mn></msqrt><mo>=</mo><msqrt><mfrac><mn>1</mn><mn>2</mn></mfrac></msqrt><mo>+</mo><msqrt><mfrac><mn>9</mn><mn>2</mn></mfrac></msqrt><mo>+</mo><msqrt><mfrac><mn>25</mn><mn>2</mn></mfrac></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><mn>3</mn><msqrt><mn>2</mn></msqrt><mo>+</mo><mn>5</mn><msqrt><mn>2</mn></msqrt></mrow><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><mn>9</mn><msqrt><mn>2</mn></msqrt></mrow><mn>2</mn></mfrac></mtd></mtr></mtable></math>

Free Form

Lớp 9

$\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}$

$\begin{aligned} \frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}} &= \frac{\sqrt{2}.\left(2+\sqrt{3}\right)}{2+\sqrt{4+2\sqrt{3}}}+\frac{\sqrt{2}.\left(2-\sqrt{3}\right)}{2-\sqrt{4-2\sqrt{3}}} \\ &= \frac{2\sqrt{2}+\sqrt{6}}{2+\sqrt{3}+1}+\frac{2\sqrt{2}-\sqrt{6}}{2-\sqrt{3}+1} = \frac{2\sqrt{2}+6}{3+\sqrt{3}}+\frac{2\sqrt{2}-\sqrt{6}}{3-\sqrt{3}} \\ &= \frac{\left(2\sqrt{2}+6\right)\left(3-\sqrt{3}\right)+\left(2\sqrt{2}-\sqrt{6}\right)\left(3+\sqrt{3}\right)}{3^2-\left(\sqrt{3}\right)^2} \\ &= \frac{6\sqrt{2}+3\sqrt{6}-2\sqrt{6}-3\sqrt{2}+6\sqrt{2}-3\sqrt{6}-2\sqrt{6}+3\sqrt{2}}{9-3} = \frac{12\sqrt{2}-4\sqrt{6}}{3} = 4\sqrt{2}-\frac{4}{3}\sqrt{6} \end{aligned}$

https://khoahoc.vietjack.com/question/1008977

### Câu hỏi: $\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}$ ### Lời giải: $\begin{aligned} \frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}} &= \frac{\sqrt{2}.\left(2+\sqrt{3}\right)}{2+\sqrt{4+2\sqrt{3}}}+\frac{\sqrt{2}.\left(2-\sqrt{3}\right)}{2-\sqrt{4-2\sqrt{3}}} \\ &= \frac{2\sqrt{2}+\sqrt{6}}{2+\sqrt{3}+1}+\frac{2\sqrt{2}-\sqrt{6}}{2-\sqrt{3}+1} = \frac{2\sqrt{2}+6}{3+\sqrt{3}}+\frac{2\sqrt{2}-\sqrt{6}}{3-\sqrt{3}} \\ &= \frac{\left(2\sqrt{2}+6\right)\left(3-\sqrt{3}\right)+\left(2\sqrt{2}-\sqrt{6}\right)\left(3+\sqrt{3}\right)}{3^2-\left(\sqrt{3}\right)^2} \\ &= \frac{6\sqrt{2}+3\sqrt{6}-2\sqrt{6}-3\sqrt{2}+6\sqrt{2}-3\sqrt{6}-2\sqrt{6}+3\sqrt{2}}{9-3} = \frac{12\sqrt{2}-4\sqrt{6}}{3} = 4\sqrt{2}-\frac{4}{3}\sqrt{6} \end{aligned}$

Free Form

Lớp 9

Rút gọn các căn thức sau: $ \sqrt{7-4\sqrt{3}}-\sqrt{7+4\sqrt{3}}$

$ \begin{array}{l}\sqrt{7-4\sqrt{3}}-\sqrt{7+4\sqrt{3}}\\ =\sqrt{{\left(\sqrt{3}-2\right)}^{2}}-\sqrt{{\left(\sqrt{3}+2\right)}^{2}}=\left|\sqrt{3}-2\right|-\left|\sqrt{3}+2\right|\\ =\sqrt{3}-2-\sqrt{3}-2=-4\end{array}$

https://khoahoc.vietjack.com/question/1008984

### Câu hỏi: Rút gọn các căn thức sau: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>7</mn><mo>−</mo><mn>4</mn><msqrt><mn>3</mn></msqrt></msqrt><mo>−</mo><msqrt><mn>7</mn><mo>+</mo><mn>4</mn><msqrt><mn>3</mn></msqrt></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>7</mn><mo>−</mo><mn>4</mn><msqrt><mn>3</mn></msqrt></msqrt><mo>−</mo><msqrt><mn>7</mn><mo>+</mo><mn>4</mn><msqrt><mn>3</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msup><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>−</mo><msqrt><msup><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>=</mo><mfenced close="|" open="|"><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>2</mn></mrow></mfenced><mo>−</mo><mfenced close="|" open="|"><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>2</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>2</mn><mo>=</mo><mo>−</mo><mn>4</mn></mtd></mtr></mtable></math>

Free Form

Lớp 9

$ \begin{array}{l}\text{\hspace{0.17em}}\left(\frac{\sqrt{38}-\sqrt{19}}{1-\sqrt{2}}+\frac{\sqrt{45}-\sqrt{15}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{19}-\sqrt{15}}\end{array}$

$ \begin{array}{l}\left(\frac{\sqrt{38}-\sqrt{19}}{1-\sqrt{2}}+\frac{\sqrt{45}-\sqrt{15}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{19}-\sqrt{15}}\\ =\left[\frac{-\sqrt{19}\left(1-\sqrt{2}\right)}{1-\sqrt{2}}-\frac{\sqrt{15}\left(1-\sqrt{3}\right)}{1-\sqrt{3}}\right].\frac{\sqrt{19}-\sqrt{15}}{1}\\ =\left(-\sqrt{19}-\sqrt{15}\right).\left(\sqrt{19}-\sqrt{15}\right)\\ =-\left(\sqrt{19}+\sqrt{15}\right).\left(\sqrt{19}-\sqrt{15}\right)=-4\text{\hspace{0.17em}}\end{array}$

https://khoahoc.vietjack.com/question/1008988

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mtext> </mtext><mfenced><mrow><mfrac><mrow><msqrt><mn>38</mn></msqrt><mo>−</mo><msqrt><mn>19</mn></msqrt></mrow><mrow><mn>1</mn><mo>−</mo><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mrow><msqrt><mn>45</mn></msqrt><mo>−</mo><msqrt><mn>15</mn></msqrt></mrow><mrow><mn>1</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac></mrow></mfenced><mo>:</mo><mfrac><mn>1</mn><mrow><msqrt><mn>19</mn></msqrt><mo>−</mo><msqrt><mn>15</mn></msqrt></mrow></mfrac></mtd></mtr></mtable></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfenced><mrow><mfrac><mrow><msqrt><mn>38</mn></msqrt><mo>−</mo><msqrt><mn>19</mn></msqrt></mrow><mrow><mn>1</mn><mo>−</mo><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mrow><msqrt><mn>45</mn></msqrt><mo>−</mo><msqrt><mn>15</mn></msqrt></mrow><mrow><mn>1</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac></mrow></mfenced><mo>:</mo><mfrac><mn>1</mn><mrow><msqrt><mn>19</mn></msqrt><mo>−</mo><msqrt><mn>15</mn></msqrt></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfenced close="]" open="["><mrow><mfrac><mrow><mo>−</mo><msqrt><mn>19</mn></msqrt><mfenced><mrow><mn>1</mn><mo>−</mo><msqrt><mn>2</mn></msqrt></mrow></mfenced></mrow><mrow><mn>1</mn><mo>−</mo><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo>−</mo><mfrac><mrow><msqrt><mn>15</mn></msqrt><mfenced><mrow><mn>1</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced></mrow><mrow><mn>1</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac></mrow></mfenced><mo>.</mo><mfrac><mrow><msqrt><mn>19</mn></msqrt><mo>−</mo><msqrt><mn>15</mn></msqrt></mrow><mn>1</mn></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mo>−</mo><msqrt><mn>19</mn></msqrt><mo>−</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><mo>.</mo><mfenced><mrow><msqrt><mn>19</mn></msqrt><mo>−</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mo>−</mo><mfenced><mrow><msqrt><mn>19</mn></msqrt><mo>+</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><mo>.</mo><mfenced><mrow><msqrt><mn>19</mn></msqrt><mo>−</mo><msqrt><mn>15</mn></msqrt></mrow></mfenced><mo>=</mo><mo>−</mo><mn>4</mn><mtext> </mtext></mtd></mtr></mtable></math>

Free Form

Lớp 9

$ D=\left(\frac{2\sqrt{x}+x}{x\sqrt{x}-1}-\frac{1}{\sqrt{x}-1}\right):\left(1-\frac{\sqrt{x}+2}{x+\sqrt{x}+1}\right)\left(\begin{array}{l}x>0\\ x\ne 1\end{array}\right)$

$ \begin{array}{l}D=\left(\frac{2\sqrt{x}+2}{x\sqrt{x}-1}-\frac{1}{\sqrt{x}-1}\right):\left(1-\frac{\sqrt{x}+2}{x+\sqrt{x}+1}\right)\left(\begin{array}{l}x>0\\ x\ne 1\end{array}\right)\\ =\frac{2\sqrt{x}+x-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}.\frac{x+\sqrt{x}+1}{x-1}\\ =\frac{\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x-1\right)}=\frac{1}{x-1}\end{array}$

https://khoahoc.vietjack.com/question/1008991

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mfenced><mrow><mfrac><mrow><mn>2</mn><msqrt><mi>x</mi></msqrt><mo>+</mo><mi>x</mi></mrow><mrow><mi>x</mi><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac><mo>−</mo><mfrac><mn>1</mn><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac></mrow></mfenced><mo>:</mo><mfenced><mrow><mn>1</mn><mo>−</mo><mfrac><mrow><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>+</mo><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>1</mn></mrow></mfrac></mrow></mfenced><mfenced><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>&gt;</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>≠</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi>D</mi><mo>=</mo><mfenced><mrow><mfrac><mrow><mn>2</mn><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>2</mn></mrow><mrow><mi>x</mi><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac><mo>−</mo><mfrac><mn>1</mn><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>1</mn></mrow></mfrac></mrow></mfenced><mo>:</mo><mfenced><mrow><mn>1</mn><mo>−</mo><mfrac><mrow><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>2</mn></mrow><mrow><mi>x</mi><mo>+</mo><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>1</mn></mrow></mfrac></mrow></mfenced><mfenced><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>&gt;</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>x</mi><mo>≠</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mn>2</mn><msqrt><mi>x</mi></msqrt><mo>+</mo><mi>x</mi><mo>−</mo><mi>x</mi><mo>−</mo><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>1</mn></mrow><mrow><mfenced><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>.</mo><mfrac><mrow><mi>x</mi><mo>+</mo><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>1</mn></mrow><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>1</mn></mrow><mrow><mfenced><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mtd></mtr></mtable></math>

Free Form

Lớp 9

Rút gọn $ A=\sqrt{\frac{m}{1-2x+{x}^{2}}}+\sqrt{\frac{4m-8mx+4m{x}^{2}}{81}}\left(\begin{array}{l}x>1\\ m\ge 0\end{array}\right)$

$ \begin{array}{l}A=\sqrt{\frac{m}{1-2x+{x}^{2}}}+\sqrt{\frac{4m-8mx+4m{x}^{2}}{81}}\left(\begin{array}{l}x>0\\ m\ge 0\end{array}\right)\\ =\frac{\sqrt{m}}{\sqrt{{\left(x-1\right)}^{2}}}+\frac{\sqrt{4m}.\sqrt{{x}^{2}-2x+1}}{\sqrt{81}}=\frac{\sqrt{m}}{x-1}+\frac{2\sqrt{m}.(x-1)}{9}\\ =\frac{9\sqrt{m}+2\sqrt{m}{\left(x-1\right)}^{2}}{9\left(x-1\right)}\end{array}$

https://khoahoc.vietjack.com/question/1008994

### Câu hỏi: Rút gọn <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><msqrt><mfrac><mi>m</mi><mrow><mn>1</mn><mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></mfrac></msqrt><mo>+</mo><msqrt><mfrac><mrow><mn>4</mn><mi>m</mi><mo>−</mo><mn>8</mn><mi>m</mi><mi>x</mi><mo>+</mo><mn>4</mn><mi>m</mi><msup><mi>x</mi><mn>2</mn></msup></mrow><mn>81</mn></mfrac></msqrt><mfenced><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>&gt;</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>m</mi><mo>≥</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi>A</mi><mo>=</mo><msqrt><mfrac><mi>m</mi><mrow><mn>1</mn><mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></mfrac></msqrt><mo>+</mo><msqrt><mfrac><mrow><mn>4</mn><mi>m</mi><mo>−</mo><mn>8</mn><mi>m</mi><mi>x</mi><mo>+</mo><mn>4</mn><mi>m</mi><msup><mi>x</mi><mn>2</mn></msup></mrow><mn>81</mn></mfrac></msqrt><mfenced><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>&gt;</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>m</mi><mo>≥</mo><mn>0</mn></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><msqrt><mi>m</mi></msqrt><msqrt><msup><mfenced><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt></mfrac><mo>+</mo><mfrac><mrow><msqrt><mn>4</mn><mi>m</mi></msqrt><mo>.</mo><msqrt><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></msqrt></mrow><msqrt><mn>81</mn></msqrt></mfrac><mo>=</mo><mfrac><msqrt><mi>m</mi></msqrt><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><msqrt><mi>m</mi></msqrt><mo>.</mo><mo>(</mo><mi>x</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mn>9</mn></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mn>9</mn><msqrt><mi>m</mi></msqrt><mo>+</mo><mn>2</mn><msqrt><mi>m</mi></msqrt><msup><mfenced><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></mrow><mrow><mn>9</mn><mfenced><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></mtd></mtr></mtable></math>

Free Form

Lớp 9

Rút gọn $ B=\sqrt{64a{b}^{3}}-3\sqrt{121{a}^{3}{b}^{3}}+2ab\sqrt{9ab}-5b\sqrt{81{a}^{3}b}\left(a,b>0\right)$

$ \begin{array}{l}B=\sqrt{64a{b}^{3}}-3\sqrt{121{a}^{3}{b}^{3}}+2ab\sqrt{9ab}-5b\sqrt{81{a}^{3}b}\\ =8b\sqrt{ab}-3.11ab\sqrt{ab}+2.3ab\sqrt{ab}-5b.9a\sqrt{ab}\\ =8b\sqrt{ab}-33ab\sqrt{ab}+6ab\sqrt{ab}-45ab\sqrt{ab}\\ =8b\sqrt{ab}-72ab\sqrt{ab}\end{array}$

https://khoahoc.vietjack.com/question/1008996

### Câu hỏi: Rút gọn <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><msqrt><mn>64</mn><mi>a</mi><msup><mi>b</mi><mn>3</mn></msup></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>121</mn><msup><mi>a</mi><mn>3</mn></msup><msup><mi>b</mi><mn>3</mn></msup></msqrt><mo>+</mo><mn>2</mn><mi>a</mi><mi>b</mi><msqrt><mn>9</mn><mi>a</mi><mi>b</mi></msqrt><mo>−</mo><mn>5</mn><mi>b</mi><msqrt><mn>81</mn><msup><mi>a</mi><mn>3</mn></msup><mi>b</mi></msqrt><mfenced><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>&gt;</mo><mn>0</mn></mrow></mfenced></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi>B</mi><mo>=</mo><msqrt><mn>64</mn><mi>a</mi><msup><mi>b</mi><mn>3</mn></msup></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>121</mn><msup><mi>a</mi><mn>3</mn></msup><msup><mi>b</mi><mn>3</mn></msup></msqrt><mo>+</mo><mn>2</mn><mi>a</mi><mi>b</mi><msqrt><mn>9</mn><mi>a</mi><mi>b</mi></msqrt><mo>−</mo><mn>5</mn><mi>b</mi><msqrt><mn>81</mn><msup><mi>a</mi><mn>3</mn></msup><mi>b</mi></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mn>8</mn><mi>b</mi><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>−</mo><mn>3.11</mn><mi>a</mi><mi>b</mi><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>+</mo><mn>2.3</mn><mi>a</mi><mi>b</mi><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>−</mo><mn>5</mn><mi>b</mi><mn>.9</mn><mi>a</mi><msqrt><mi>a</mi><mi>b</mi></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mn>8</mn><mi>b</mi><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>−</mo><mn>33</mn><mi>a</mi><mi>b</mi><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>+</mo><mn>6</mn><mi>a</mi><mi>b</mi><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>−</mo><mn>45</mn><mi>a</mi><mi>b</mi><msqrt><mi>a</mi><mi>b</mi></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mn>8</mn><mi>b</mi><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>−</mo><mn>72</mn><mi>a</mi><mi>b</mi><msqrt><mi>a</mi><mi>b</mi></msqrt></mtd></mtr></mtable></math>

Free Form

Lớp 9

$ S=\left(\frac{\sqrt{a}+a}{1+\sqrt{a}}\right).\left(\frac{a-3\sqrt{a}+2}{\sqrt{a}-2}\right)\left(\begin{array}{l}a>0\\ a\ne 4\end{array}\right)$

$ \begin{array}{l}S=\left(\frac{\sqrt{a}+a}{1+\sqrt{a}}\right).\left(\frac{a-3\sqrt{a}+2}{\sqrt{a}-2}\right)\left(\begin{array}{l}a>0\\ a\ne 4\end{array}\right)\\ =\frac{\sqrt{a}.\left(1+\sqrt{a}\right)}{1+\sqrt{a}}.\frac{a-\sqrt{a}-2\sqrt{a}+2}{\sqrt{a}-2}\\ =\sqrt{a}.\frac{\left(\sqrt{a}-1\right)\left(\sqrt{a}-2\right)}{\sqrt{a}-2}=\sqrt{a}.\left(\sqrt{a}-1\right)=a-\sqrt{a}\end{array}$

https://khoahoc.vietjack.com/question/1008999

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mfenced><mfrac><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><mi>a</mi></mrow><mrow><mn>1</mn><mo>+</mo><msqrt><mi>a</mi></msqrt></mrow></mfrac></mfenced><mo>.</mo><mfenced><mfrac><mrow><mi>a</mi><mo>−</mo><mn>3</mn><msqrt><mi>a</mi></msqrt><mo>+</mo><mn>2</mn></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><mn>2</mn></mrow></mfrac></mfenced><mfenced><mtable columnalign="left"><mtr><mtd><mi>a</mi><mo>&gt;</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>a</mi><mo>≠</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi>S</mi><mo>=</mo><mfenced><mfrac><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><mi>a</mi></mrow><mrow><mn>1</mn><mo>+</mo><msqrt><mi>a</mi></msqrt></mrow></mfrac></mfenced><mo>.</mo><mfenced><mfrac><mrow><mi>a</mi><mo>−</mo><mn>3</mn><msqrt><mi>a</mi></msqrt><mo>+</mo><mn>2</mn></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><mn>2</mn></mrow></mfrac></mfenced><mfenced><mtable columnalign="left"><mtr><mtd><mi>a</mi><mo>&gt;</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>a</mi><mo>≠</mo><mn>4</mn></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><msqrt><mi>a</mi></msqrt><mo>.</mo><mfenced><mrow><mn>1</mn><mo>+</mo><msqrt><mi>a</mi></msqrt></mrow></mfenced></mrow><mrow><mn>1</mn><mo>+</mo><msqrt><mi>a</mi></msqrt></mrow></mfrac><mo>.</mo><mfrac><mrow><mi>a</mi><mo>−</mo><msqrt><mi>a</mi></msqrt><mo>−</mo><mn>2</mn><msqrt><mi>a</mi></msqrt><mo>+</mo><mn>2</mn></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><mn>2</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mi>a</mi></msqrt><mo>.</mo><mfrac><mrow><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><mn>2</mn></mrow></mfenced></mrow><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><mn>2</mn></mrow></mfrac><mo>=</mo><msqrt><mi>a</mi></msqrt><mo>.</mo><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mo>=</mo><mi>a</mi><mo>−</mo><msqrt><mi>a</mi></msqrt></mtd></mtr></mtable></math>

Free Form

Lớp 9

$\sqrt{4x^2-4x+1}-\sqrt{9x^2}=0$

$\begin{aligned} \sqrt{4x^2-4x+1}-\sqrt{9x^2}&=0\\ \Leftrightarrow \sqrt{(2x-1)^2}-\sqrt{(3x)^2}&=0\\ \Leftrightarrow |2x-1|&=|3x|\\ \Leftrightarrow \left[ \begin{aligned} 2x-1&=3x\\ 2x-1&=-3x \end{aligned} \right. \Rightarrow \left[ \begin{aligned} x&=-1\\ x&=\frac{1}{5} \end{aligned} \right. \end{aligned}$

https://khoahoc.vietjack.com/question/1009002

### Câu hỏi: $\sqrt{4x^2-4x+1}-\sqrt{9x^2}=0$ ### Lời giải: $\begin{aligned} \sqrt{4x^2-4x+1}-\sqrt{9x^2}&=0\\ \Leftrightarrow \sqrt{(2x-1)^2}-\sqrt{(3x)^2}&=0\\ \Leftrightarrow |2x-1|&=|3x|\\ \Leftrightarrow \left[ \begin{aligned} 2x-1&=3x\\ 2x-1&=-3x \end{aligned} \right. \Rightarrow \left[ \begin{aligned} x&=-1\\ x&=\frac{1}{5} \end{aligned} \right. \end{aligned}$

Free Form

Lớp 9

$\sqrt{3x-5}+\sqrt{2x-3}=\sqrt{x+2}$

$\begin{aligned} \sqrt{3x-5}+\sqrt{2x-3}&=\sqrt{x+2} \left(x\geq \frac{5}{3}\right)\\ \Leftrightarrow \sqrt{3x-5}&=\sqrt{x+2}-\sqrt{2x-3}\\ \Rightarrow 3x-5&=x+2+2x-3-2\sqrt{(x+2)(2x-3)}\\ \Leftrightarrow \sqrt{(x+2)(2x-3)}&=2 \Leftrightarrow 2x^2+x-6=4\\ \Leftrightarrow 2x^2+x-10&=0 \Leftrightarrow \left[ \begin{aligned} x&=2 (tm)\\ x&=-\frac{5}{2} (ktm) \end{aligned} \right. \end{aligned}$

https://khoahoc.vietjack.com/question/1009005

### Câu hỏi: $\sqrt{3x-5}+\sqrt{2x-3}=\sqrt{x+2}$ ### Lời giải: $\begin{aligned} \sqrt{3x-5}+\sqrt{2x-3}&=\sqrt{x+2} \left(x\geq \frac{5}{3}\right)\\ \Leftrightarrow \sqrt{3x-5}&=\sqrt{x+2}-\sqrt{2x-3}\\ \Rightarrow 3x-5&=x+2+2x-3-2\sqrt{(x+2)(2x-3)}\\ \Leftrightarrow \sqrt{(x+2)(2x-3)}&=2 \Leftrightarrow 2x^2+x-6=4\\ \Leftrightarrow 2x^2+x-10&=0 \Leftrightarrow \left[ \begin{aligned} x&=2 (tm)\\ x&=-\frac{5}{2} (ktm) \end{aligned} \right. \end{aligned}$

Free Form

Lớp 9

$ \frac{2{x}^{2}}{3-\sqrt{{\left(9+2x\right)}^{2}}}=x+9$

$ \frac{2{x}^{2}}{3-\sqrt{{\left(9+2x\right)}^{2}}}=x+9\Leftrightarrow \frac{2{x}^{2}}{3-\left|9+2x\right|}=x+9$ $ \begin{array}{l}x\ge \frac{-9}{2}\Rightarrow \frac{2{x}^{2}}{3-9-2x}=x+9\\ \Leftrightarrow 2{x}^{2}+24x=-54+2{x}^{2}\\ \Rightarrow x=-\frac{9}{4}\left(tm\right)\\ x<-\frac{9}{2}\Rightarrow \frac{2{x}^{2}}{3+9+2x}=x+9\\ \Leftrightarrow 2{x}^{2}=2{x}^{2}+30x+108\\ \Rightarrow x=-\frac{-18}{5}\left(ktm\right)\text{\hspace{0.17em}\hspace{0.17em}}Vay\text{\hspace{0.17em}}x=\frac{-9}{4}\end{array}$

https://khoahoc.vietjack.com/question/1009010

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><mrow><mn>3</mn><mo>−</mo><msqrt><msup><mfenced><mrow><mn>9</mn><mo>+</mo><mn>2</mn><mi>x</mi></mrow></mfenced><mn>2</mn></msup></msqrt></mrow></mfrac><mo>=</mo><mi>x</mi><mo>+</mo><mn>9</mn></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><mrow><mn>3</mn><mo>−</mo><msqrt><msup><mfenced><mrow><mn>9</mn><mo>+</mo><mn>2</mn><mi>x</mi></mrow></mfenced><mn>2</mn></msup></msqrt></mrow></mfrac><mo>=</mo><mi>x</mi><mo>+</mo><mn>9</mn><mo>⇔</mo><mfrac><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><mrow><mn>3</mn><mo>−</mo><mfenced close="|" open="|"><mrow><mn>9</mn><mo>+</mo><mn>2</mn><mi>x</mi></mrow></mfenced></mrow></mfrac><mo>=</mo><mi>x</mi><mo>+</mo><mn>9</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>≥</mo><mfrac><mrow><mo>−</mo><mn>9</mn></mrow><mn>2</mn></mfrac><mo>⇒</mo><mfrac><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><mrow><mn>3</mn><mo>−</mo><mn>9</mn><mo>−</mo><mn>2</mn><mi>x</mi></mrow></mfrac><mo>=</mo><mi>x</mi><mo>+</mo><mn>9</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>24</mn><mi>x</mi><mo>=</mo><mo>−</mo><mn>54</mn><mo>+</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mo>⇒</mo><mi>x</mi><mo>=</mo><mo>−</mo><mfrac><mn>9</mn><mn>4</mn></mfrac><mo>(</mo><mi>t</mi><mi>m</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>x</mi><mo>&lt;</mo><mo>−</mo><mfrac><mn>9</mn><mn>2</mn></mfrac><mo>⇒</mo><mfrac><mrow><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><mrow><mn>3</mn><mo>+</mo><mn>9</mn><mo>+</mo><mn>2</mn><mi>x</mi></mrow></mfrac><mo>=</mo><mi>x</mi><mo>+</mo><mn>9</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>30</mn><mi>x</mi><mo>+</mo><mn>108</mn></mtd></mtr><mtr><mtd><mo>⇒</mo><mi>x</mi><mo>=</mo><mo>−</mo><mfrac><mrow><mo>−</mo><mn>18</mn></mrow><mn>5</mn></mfrac><mo>(</mo><mi>k</mi><mi>t</mi><mi>m</mi><mo>)</mo><mtext>  </mtext><mi>V</mi><mi>a</mi><mi>y</mi><mtext> </mtext><mi>x</mi><mo>=</mo><mfrac><mrow><mo>−</mo><mn>9</mn></mrow><mn>4</mn></mfrac></mtd></mtr></mtable></math>

Free Form

Lớp 9

Giải phương trình: $ 4\sqrt{2x}-2\sqrt{18x}+\sqrt{32x}=3$

$ \begin{array}{l}4\sqrt{2x}-2\sqrt{18x}+\sqrt{32x}=3\\ \Leftrightarrow 4\sqrt{2x}-2.3\sqrt{2x}+4\sqrt{2x}=3\left(x\ge 0\right)\\ \Leftrightarrow 2\sqrt{2x}=3\Rightarrow 2x=\frac{9}{4}\Rightarrow x=\frac{9}{8}\left(tm\right)\end{array}$

https://khoahoc.vietjack.com/question/1009011

### Câu hỏi: Giải phương trình: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><msqrt><mn>2</mn><mi>x</mi></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>18</mn><mi>x</mi></msqrt><mo>+</mo><msqrt><mn>32</mn><mi>x</mi></msqrt><mo>=</mo><mn>3</mn></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mn>4</mn><msqrt><mn>2</mn><mi>x</mi></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>18</mn><mi>x</mi></msqrt><mo>+</mo><msqrt><mn>32</mn><mi>x</mi></msqrt><mo>=</mo><mn>3</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>4</mn><msqrt><mn>2</mn><mi>x</mi></msqrt><mo>−</mo><mn>2.3</mn><msqrt><mn>2</mn><mi>x</mi></msqrt><mo>+</mo><mn>4</mn><msqrt><mn>2</mn><mi>x</mi></msqrt><mo>=</mo><mn>3</mn><mfenced><mrow><mi>x</mi><mo>≥</mo><mn>0</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>2</mn><msqrt><mn>2</mn><mi>x</mi></msqrt><mo>=</mo><mn>3</mn><mo>⇒</mo><mn>2</mn><mi>x</mi><mo>=</mo><mfrac><mn>9</mn><mn>4</mn></mfrac><mo>⇒</mo><mi>x</mi><mo>=</mo><mfrac><mn>9</mn><mn>8</mn></mfrac><mo>(</mo><mi>t</mi><mi>m</mi><mo>)</mo></mtd></mtr></mtable></math>

Free Form

Lớp 9

$ \sqrt{x+4}+\sqrt{x-1}=2$

$ \begin{array}{l}\\ x+4+x-1+2\sqrt{\left(x+4\right)\left(x-1\right)}=2\\ \Leftrightarrow 4\left(x+4\right)\left(x-1\right)={\left(-2x-1\right)}^{2}\\ \Leftrightarrow 4{x}^{2}+12x-16=4{x}^{2}+4x+1\\ \Leftrightarrow x=\frac{17}{8}\left(tm\right)\end{array}$

https://khoahoc.vietjack.com/question/1009017

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>x</mi><mo>+</mo><mn>4</mn></msqrt><mo>+</mo><msqrt><mi>x</mi><mo>−</mo><mn>1</mn></msqrt><mo>=</mo><mn>2</mn></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd></mtd></mtr><mtr><mtd><mi>x</mi><mo>+</mo><mn>4</mn><mo>+</mo><mi>x</mi><mo>−</mo><mn>1</mn><mo>+</mo><mn>2</mn><msqrt><mfenced><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfenced></msqrt><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>4</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfenced><mo>=</mo><msup><mfenced><mrow><mo>−</mo><mn>2</mn><mi>x</mi><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></mtd></mtr><mtr><mtd><mo>⇔</mo><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><mi>x</mi><mo>−</mo><mn>16</mn><mo>=</mo><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mi>x</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mo>⇔</mo><mi>x</mi><mo>=</mo><mfrac><mn>17</mn><mn>8</mn></mfrac><mo>(</mo><mi>t</mi><mi>m</mi><mo>)</mo></mtd></mtr></mtable></math>

Free Form

Lớp 9

$\sqrt{44}-\sqrt{176}+2\sqrt{275}$

$\sqrt{44}-\sqrt{176}+2\sqrt{275}=2\sqrt{11}-4\sqrt{11}+10\sqrt{11}=8\sqrt{11}$

https://khoahoc.vietjack.com/question/1009018

### Câu hỏi: $\sqrt{44}-\sqrt{176}+2\sqrt{275}$ ### Lời giải: $\sqrt{44}-\sqrt{176}+2\sqrt{275}=2\sqrt{11}-4\sqrt{11}+10\sqrt{11}=8\sqrt{11}$

Free Form

Lớp 9

<p>Tính</p> <p>$ 5\sqrt{3}-3\sqrt{48}+2\sqrt{75}-\frac{1}{3}\sqrt{108}$</p>

<p>$ 5\sqrt{3}-3\sqrt{48}+2\sqrt{75}-\frac{1}{3}\sqrt{108}=5\sqrt{3}-12\sqrt{3}+10\sqrt{3}-2\sqrt{3}=\sqrt{3}$</p>

https://khoahoc.vietjack.com/question/1009020

### Câu hỏi: <p>Tính</p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>48</mn></msqrt><mo>+</mo><mn>2</mn><msqrt><mn>75</mn></msqrt><mo>−</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msqrt><mn>108</mn></msqrt></math></p> ### Lời giải: <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>48</mn></msqrt><mo>+</mo><mn>2</mn><msqrt><mn>75</mn></msqrt><mo>−</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><msqrt><mn>108</mn></msqrt><mo>=</mo><mn>5</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>12</mn><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>10</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>3</mn></msqrt><mo>=</mo><msqrt><mn>3</mn></msqrt></math></p>

Free Form

Lớp 9

<p>Tính</p> <p>$ \sqrt{343}-\sqrt{112}-\sqrt{63}-\sqrt{21}$</p>

<p>$ \sqrt{343}-\sqrt{112}-\sqrt{63}-\sqrt{21}=7\sqrt{7}-4\sqrt{7}-3\sqrt{7}-\sqrt{21}=-\sqrt{21}$</p>

https://khoahoc.vietjack.com/question/1009023

### Câu hỏi: <p>Tính</p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>343</mn></msqrt><mo>−</mo><msqrt><mn>112</mn></msqrt><mo>−</mo><msqrt><mn>63</mn></msqrt><mo>−</mo><msqrt><mn>21</mn></msqrt></math></p> ### Lời giải: <p><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>343</mn></msqrt><mo>−</mo><msqrt><mn>112</mn></msqrt><mo>−</mo><msqrt><mn>63</mn></msqrt><mo>−</mo><msqrt><mn>21</mn></msqrt><mo>=</mo><mn>7</mn><msqrt><mn>7</mn></msqrt><mo>−</mo><mn>4</mn><msqrt><mn>7</mn></msqrt><mo>−</mo><mn>3</mn><msqrt><mn>7</mn></msqrt><mo>−</mo><msqrt><mn>21</mn></msqrt><mo>=</mo><mo>−</mo><msqrt><mn>21</mn></msqrt></math></p>

Free Form

Lớp 9

<p>Tính</p> $ \sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{4+2\sqrt{3}}}}$

$ \begin{array}{l}\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{4+2\sqrt{3}}}}=\sqrt{6+2\sqrt{2}.\sqrt{3-\left(\sqrt{3}+1\right)}}\\ =\sqrt{6+2\sqrt{2}.\sqrt{2-\sqrt{3}}}=\sqrt{6+2\sqrt{4-2\sqrt{3}}}\\ =\sqrt{6+2\left(\sqrt{3}-1\right)}=\sqrt{6+2\sqrt{3}-2}\\ =\sqrt{4+2\sqrt{3}}=\sqrt{{\left(\sqrt{3}+1\right)}^{2}}=\sqrt{3}+1\end{array}$

https://khoahoc.vietjack.com/question/1009024

### Câu hỏi: <p>Tính</p> <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>6</mn><mo>+</mo><mn>2</mn><msqrt><mn>2</mn></msqrt><mo>.</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>4</mn><mo>+</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></msqrt></msqrt></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>6</mn><mo>+</mo><mn>2</mn><msqrt><mn>2</mn></msqrt><mo>.</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>4</mn><mo>+</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></msqrt></msqrt></msqrt><mo>=</mo><msqrt><mn>6</mn><mo>+</mo><mn>2</mn><msqrt><mn>2</mn></msqrt><mo>.</mo><msqrt><mn>3</mn><mo>−</mo><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>6</mn><mo>+</mo><mn>2</mn><msqrt><mn>2</mn></msqrt><mo>.</mo><msqrt><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></msqrt></msqrt><mo>=</mo><msqrt><mn>6</mn><mo>+</mo><mn>2</mn><msqrt><mn>4</mn><mo>−</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>6</mn><mo>+</mo><mn>2</mn><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></msqrt><mo>=</mo><msqrt><mn>6</mn><mo>+</mo><mn>2</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>2</mn></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>4</mn><mo>+</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></msqrt><mo>=</mo><msqrt><msup><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>=</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></mtd></mtr></mtable></math>

Free Form

Lớp 9

<p>Tính</p> <p>$ \sqrt{28+\sqrt{300}}+\sqrt{19-\sqrt{192}}$</p>

<p>$ \begin{array}{l}\sqrt{28+\sqrt{300}}+\sqrt{19-\sqrt{192}}\\ =\sqrt{28+10\sqrt{3}}+\sqrt{19-8\sqrt{3}}\\ =\sqrt{{5}^{2}+\mathrm{2.5.}\sqrt{3}+{\left(\sqrt{3}\right)}^{2}}+\sqrt{{4}^{2}-\mathrm{2.4.}\sqrt{3}+{\left(\sqrt{3}\right)}^{2}}\\ =\sqrt{{\left(5+\sqrt{3}\right)}^{2}}+\sqrt{{\left(4-\sqrt{3}\right)}^{2}}\\ =5+\sqrt{3}+4-\sqrt{3}=9\end{array}$</p>

https://khoahoc.vietjack.com/question/1009028

### Câu hỏi: <p>Tính</p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>28</mn><mo>+</mo><msqrt><mn>300</mn></msqrt></msqrt><mo>+</mo><msqrt><mn>19</mn><mo>−</mo><msqrt><mn>192</mn></msqrt></msqrt></math></p> ### Lời giải: <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msqrt><mn>28</mn><mo>+</mo><msqrt><mn>300</mn></msqrt></msqrt><mo>+</mo><msqrt><mn>19</mn><mo>−</mo><msqrt><mn>192</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>28</mn><mo>+</mo><mn>10</mn><msqrt><mn>3</mn></msqrt></msqrt><mo>+</mo><msqrt><mn>19</mn><mo>−</mo><mn>8</mn><msqrt><mn>3</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msup><mn>5</mn><mn>2</mn></msup><mo>+</mo><mn>2.5.</mn><msqrt><mn>3</mn></msqrt><mo>+</mo><msup><mfenced><msqrt><mn>3</mn></msqrt></mfenced><mn>2</mn></msup></msqrt><mo>+</mo><msqrt><msup><mn>4</mn><mn>2</mn></msup><mo>−</mo><mn>2.4.</mn><msqrt><mn>3</mn></msqrt><mo>+</mo><msup><mfenced><msqrt><mn>3</mn></msqrt></mfenced><mn>2</mn></msup></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msup><mfenced><mrow><mn>5</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mn>2</mn></msup></msqrt><mo>+</mo><msqrt><msup><mfenced><mrow><mn>4</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mn>2</mn></msup></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mn>5</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>4</mn><mo>−</mo><msqrt><mn>3</mn></msqrt><mo>=</mo><mn>9</mn></mtd></mtr></mtable></math></p>

Free Form

Lớp 9

<p>Tính</p> <div>$ \begin{array}{l}\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}+\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}\end{array}$</div>

<div>$ \begin{array}{l}\frac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}+\frac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}=\frac{{\left(\sqrt{7}+\sqrt{5}\right)}^{2}+{\left(\sqrt{7}-\sqrt{5}\right)}^{2}}{\left(\sqrt{7}-\sqrt{5}\right)\left(\sqrt{7}+\sqrt{5}\right)}\\ =\frac{12+2\sqrt{35}+12-2\sqrt{35}}{7-5}=\frac{24}{2}=12\end{array}$</div>

https://khoahoc.vietjack.com/question/1009034

### Câu hỏi: <p>Tính</p> <div><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfrac><mrow><msqrt><mn>7</mn></msqrt><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow><mrow><msqrt><mn>7</mn></msqrt><mo>−</mo><msqrt><mn>5</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mrow><msqrt><mn>7</mn></msqrt><mo>−</mo><msqrt><mn>5</mn></msqrt></mrow><mrow><msqrt><mn>7</mn></msqrt><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfrac></mtd></mtr></mtable></math></div> ### Lời giải: <div><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfrac><mrow><msqrt><mn>7</mn></msqrt><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow><mrow><msqrt><mn>7</mn></msqrt><mo>−</mo><msqrt><mn>5</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mrow><msqrt><mn>7</mn></msqrt><mo>−</mo><msqrt><mn>5</mn></msqrt></mrow><mrow><msqrt><mn>7</mn></msqrt><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><msup><mfenced><mrow><msqrt><mn>7</mn></msqrt><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><msqrt><mn>7</mn></msqrt><mo>−</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mn>2</mn></msup></mrow><mrow><mfenced><mrow><msqrt><mn>7</mn></msqrt><mo>−</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mn>7</mn></msqrt><mo>+</mo><msqrt><mn>5</mn></msqrt></mrow></mfenced></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mn>12</mn><mo>+</mo><mn>2</mn><msqrt><mn>35</mn></msqrt><mo>+</mo><mn>12</mn><mo>−</mo><mn>2</mn><msqrt><mn>35</mn></msqrt></mrow><mrow><mn>7</mn><mo>−</mo><mn>5</mn></mrow></mfrac><mo>=</mo><mfrac><mn>24</mn><mn>2</mn></mfrac><mo>=</mo><mn>12</mn></mtd></mtr></mtable></math></div>

Free Form

Lớp 9

Phân tích đa thức thành nhân tử $ a+\sqrt{a}+2\sqrt{ab}+2\sqrt{b}$

$ \begin{array}{l}a+\sqrt{a}+2\sqrt{ab}+2\sqrt{b}\\ =\sqrt{a}\left(\sqrt{a}+1\right)+2\sqrt{b}\left(\sqrt{a}+1\right)\\ =\left(\sqrt{a}+1\right)\left(\sqrt{a}+2\sqrt{b}\right)\end{array}$

https://khoahoc.vietjack.com/question/1009046

### Câu hỏi: Phân tích đa thức thành nhân tử <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>+</mo><msqrt><mi>a</mi></msqrt><mo>+</mo><mn>2</mn><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>+</mo><mn>2</mn><msqrt><mi>b</mi></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi>a</mi><mo>+</mo><msqrt><mi>a</mi></msqrt><mo>+</mo><mn>2</mn><msqrt><mi>a</mi><mi>b</mi></msqrt><mo>+</mo><mn>2</mn><msqrt><mi>b</mi></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mi>a</mi></msqrt><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mn>2</mn><msqrt><mi>b</mi></msqrt><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><msqrt><mi>a</mi></msqrt><mo>+</mo><mn>2</mn><msqrt><mi>b</mi></msqrt></mrow></mfenced></mtd></mtr></mtable></math>

Free Form

Lớp 9

$ {\left(1+\sqrt{x}\right)}^{2}-4\sqrt{x}$

$ \begin{array}{l}{\left(1+\sqrt{x}\right)}^{2}-4\sqrt{x}\\ =1+2\sqrt{x}+x-4\sqrt{x}\\ =x-2\sqrt{x}+1\\ ={\left(\sqrt{x}-1\right)}^{2}\end{array}$

https://khoahoc.vietjack.com/question/1009050

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mn>1</mn><mo>+</mo><msqrt><mi>x</mi></msqrt></mrow></mfenced><mn>2</mn></msup><mo>−</mo><mn>4</mn><msqrt><mi>x</mi></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><msup><mfenced><mrow><mn>1</mn><mo>+</mo><msqrt><mi>x</mi></msqrt></mrow></mfenced><mn>2</mn></msup><mo>−</mo><mn>4</mn><msqrt><mi>x</mi></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mn>1</mn><mo>+</mo><mn>2</mn><msqrt><mi>x</mi></msqrt><mo>+</mo><mi>x</mi><mo>−</mo><mn>4</mn><msqrt><mi>x</mi></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mi>x</mi><mo>−</mo><mn>2</mn><msqrt><mi>x</mi></msqrt><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mo>=</mo><msup><mfenced><mrow><msqrt><mi>x</mi></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></mtd></mtr></mtable></math>

Free Form

Lớp 9

$ b\sqrt{b}-4b+4\sqrt{b}-a\sqrt{b}$

$ \begin{array}{l}\text{\hspace{0.17em}}b\sqrt{b}-4b+4\sqrt{b}-a\sqrt{b}\\ =\sqrt{b}\left[\left(b-4\sqrt{b}+4\right)-a\right]=\sqrt{b}\left[{\left(\sqrt{b}-2\right)}^{2}-{\left(\sqrt{a}\right)}^{2}\right]\\ =\sqrt{b}\left(\sqrt{b}-2-\sqrt{a}\right)\left(\sqrt{b}-2+\sqrt{a}\right)\end{array}$

https://khoahoc.vietjack.com/question/1009055

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><msqrt><mi>b</mi></msqrt><mo>−</mo><mn>4</mn><mi>b</mi><mo>+</mo><mn>4</mn><msqrt><mi>b</mi></msqrt><mo>−</mo><mi>a</mi><msqrt><mi>b</mi></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mtext> </mtext><mi>b</mi><msqrt><mi>b</mi></msqrt><mo>−</mo><mn>4</mn><mi>b</mi><mo>+</mo><mn>4</mn><msqrt><mi>b</mi></msqrt><mo>−</mo><mi>a</mi><msqrt><mi>b</mi></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mi>b</mi></msqrt><mfenced close="]" open="["><mrow><mfenced><mrow><mi>b</mi><mo>−</mo><mn>4</mn><msqrt><mi>b</mi></msqrt><mo>+</mo><mn>4</mn></mrow></mfenced><mo>−</mo><mi>a</mi></mrow></mfenced><mo>=</mo><msqrt><mi>b</mi></msqrt><mfenced close="]" open="["><mrow><msup><mfenced><mrow><msqrt><mi>b</mi></msqrt><mo>−</mo><mn>2</mn></mrow></mfenced><mn>2</mn></msup><mo>−</mo><msup><mfenced><msqrt><mi>a</mi></msqrt></mfenced><mn>2</mn></msup></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mi>b</mi></msqrt><mfenced><mrow><msqrt><mi>b</mi></msqrt><mo>−</mo><mn>2</mn><mo>−</mo><msqrt><mi>a</mi></msqrt></mrow></mfenced><mfenced><mrow><msqrt><mi>b</mi></msqrt><mo>−</mo><mn>2</mn><mo>+</mo><msqrt><mi>a</mi></msqrt></mrow></mfenced></mtd></mtr></mtable></math>

Free Form

Lớp 9

Tìm x: $ \sqrt[3]{x-5}=0,9$

$ \sqrt[3]{x-5}=0,9\Leftrightarrow x-5=0,{9}^{3}\Leftrightarrow x=5,729$. Vậy x = 5,729.

https://khoahoc.vietjack.com/question/1009069

### Câu hỏi: Tìm x: <math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mrow><mi>x</mi><mo>−</mo><mn>5</mn></mrow><mn>3</mn></mroot><mo>=</mo><mn>0</mn><mo>,</mo><mn>9</mn></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mrow><mi>x</mi><mo>−</mo><mn>5</mn></mrow><mn>3</mn></mroot><mo>=</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>⇔</mo><mi>x</mi><mo>−</mo><mn>5</mn><mo>=</mo><mn>0</mn><mo>,</mo><msup><mn>9</mn><mn>3</mn></msup><mo>⇔</mo><mi>x</mi><mo>=</mo><mn>5</mn><mo>,</mo><mn>729</mn></math>. Vậy x = 5,729.

Free Form

Lớp 9

Rút gọn biểu thức : $ B=\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}$

$ \begin{array}{l}B=\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}\\ \Rightarrow B\sqrt{2}=\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\\ =\sqrt{{\left(\sqrt{5}+1\right)}^{2}}-\sqrt{{\left(\sqrt{5}-1\right)}^{2}}=\sqrt{5}+1-\left|\sqrt{5}-1\right|\\ =\sqrt{5}+1-\sqrt{5}+1=2\Rightarrow B=\sqrt{2}\left(do\text{\hspace{0.17em}}B>0\right)\end{array}$

https://khoahoc.vietjack.com/question/1009079

### Câu hỏi: Rút gọn biểu thức : <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><msqrt><mn>3</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>5</mn></msqrt></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mi>B</mi><mo>=</mo><msqrt><mn>3</mn><mo>+</mo><msqrt><mn>5</mn></msqrt></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>5</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>⇒</mo><mi>B</mi><msqrt><mn>2</mn></msqrt><mo>=</mo><msqrt><mn>6</mn><mo>+</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></msqrt><mo>−</mo><msqrt><mn>6</mn><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>−</mo><msqrt><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt><mo>=</mo><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>1</mn><mo>−</mo><mfenced close="|" open="|"><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>1</mn><mo>−</mo><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>1</mn><mo>=</mo><mn>2</mn><mo>⇒</mo><mi>B</mi><mo>=</mo><msqrt><mn>2</mn></msqrt><mfenced><mrow><mi>d</mi><mi>o</mi><mtext> </mtext><mi>B</mi><mo>&gt;</mo><mn>0</mn></mrow></mfenced></mtd></mtr></mtable></math>

Free Form

Lớp 9

$ C=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}$

$ \begin{array}{l}\text{\hspace{0.17em}}C=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\\ =\sqrt{\sqrt{5}-\sqrt{3-\sqrt{{\left(2\sqrt{5}\right)}^{2}-2.2\sqrt{5}.3+{3}^{2}}}}\\ =\sqrt{\sqrt{5}-\sqrt{3-\sqrt{{\left(2\sqrt{5}-3\right)}^{2}}}}\\ =\sqrt{\sqrt{5-\sqrt{3-\left(2\sqrt{5}-3\right)}}}\\ =\sqrt{\sqrt{5}-\sqrt{3-2\sqrt{5}+3}}\\ =\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}\\ =\sqrt{\sqrt{5}-\sqrt{{\left(\sqrt{5}-1\right)}^{2}}}=\sqrt{\sqrt{5}-\left|\sqrt{5}-1\right|}=\sqrt{\sqrt{5}-\sqrt{5}+1}=\sqrt{1}=1\end{array}$

https://khoahoc.vietjack.com/question/1009082

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>29</mn><mo>−</mo><mn>12</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mtext> </mtext><mi>C</mi><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><mn>29</mn><mo>−</mo><mn>12</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><msup><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt></mrow></mfenced><mn>2</mn></msup><mo>−</mo><mn>2.2</mn><msqrt><mn>5</mn></msqrt><mn>.3</mn><mo>+</mo><msup><mn>3</mn><mn>2</mn></msup></msqrt></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><msqrt><msup><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn></mrow></mfenced><mn>2</mn></msup></msqrt></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>5</mn><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><mfenced><mrow><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>3</mn></mrow></mfenced></msqrt></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>3</mn></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>6</mn><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></msqrt></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><msup><mfenced><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></msqrt></msqrt><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><mfenced close="|" open="|"><mrow><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></msqrt><mo>=</mo><msqrt><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>1</mn></msqrt><mo>=</mo><msqrt><mn>1</mn></msqrt><mo>=</mo><mn>1</mn></mtd></mtr></mtable></math>

Free Form

Lớp 9

$D = \sqrt{3 - \sqrt{5}} (\sqrt{10} - \sqrt{2}) (3 + \sqrt{5})$

$\begin{aligned} D &= \sqrt{3 - \sqrt{5}} (\sqrt{10} - \sqrt{2}) (3 + \sqrt{5}) \\ &= \sqrt{2(3 - \sqrt{5})} . (\sqrt{5} - 1) (3 + \sqrt{5}) \\ &= \sqrt{6 - 2\sqrt{5}} . (\sqrt{5} - 1) (3 + \sqrt{5}) \\ &= (\sqrt{5} - 1) (\sqrt{5} - 1) (3 + \sqrt{5}) \\ &= (\sqrt{5} - 1)^2 . (3 + \sqrt{5}) = (6 - 2\sqrt{5}) (3 + \sqrt{5}) \\ &= 18 - 6\sqrt{5} + 6\sqrt{5} - 10 = 8 \end{aligned}$

https://khoahoc.vietjack.com/question/1009085

### Câu hỏi: $D = \sqrt{3 - \sqrt{5}} (\sqrt{10} - \sqrt{2}) (3 + \sqrt{5})$ ### Lời giải: $\begin{aligned} D &= \sqrt{3 - \sqrt{5}} (\sqrt{10} - \sqrt{2}) (3 + \sqrt{5}) \\ &= \sqrt{2(3 - \sqrt{5})} . (\sqrt{5} - 1) (3 + \sqrt{5}) \\ &= \sqrt{6 - 2\sqrt{5}} . (\sqrt{5} - 1) (3 + \sqrt{5}) \\ &= (\sqrt{5} - 1) (\sqrt{5} - 1) (3 + \sqrt{5}) \\ &= (\sqrt{5} - 1)^2 . (3 + \sqrt{5}) = (6 - 2\sqrt{5}) (3 + \sqrt{5}) \\ &= 18 - 6\sqrt{5} + 6\sqrt{5} - 10 = 8 \end{aligned}$

Free Form

Lớp 9

$ G=\frac{1+\frac{\sqrt{3}}{2}}{1+\sqrt{1+\frac{\sqrt{3}}{2}}}+\frac{1-\frac{\sqrt{3}}{2}}{1-\sqrt{1-\frac{\sqrt{3}}{2}}}$

$ \begin{array}{l}\text{\hspace{0.17em}}G=\frac{1+\frac{\sqrt{3}}{2}}{1+\sqrt{1+\frac{\sqrt{3}}{2}}}+\frac{1-\frac{\sqrt{3}}{2}}{1-\sqrt{1-\frac{\sqrt{3}}{2}}}=\frac{\frac{2+\sqrt{3}}{2}}{\frac{\sqrt{2}+\sqrt{2+\sqrt{3}}}{\sqrt{2}}}+\frac{\frac{2-\sqrt{3}}{2}}{\frac{\sqrt{2}-\sqrt{2-\sqrt{3}}}{\sqrt{2}}}\\ =\frac{2+\sqrt{3}}{2}.\frac{\sqrt{2}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{2}.\frac{\sqrt{2}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\end{array}$ $ \begin{array}{l}=\frac{2+\sqrt{3}}{\sqrt{2}.\left(\sqrt{2}+\sqrt{2+\sqrt{3}}\right)}+\frac{2-\sqrt{3}}{\sqrt{2}.\left(\sqrt{2}-\sqrt{2-\sqrt{3}}\right)}\\ =\frac{2+\sqrt{3}}{2+\sqrt{4+2\sqrt{3}}}+\frac{2-\sqrt{3}}{2-\sqrt{4-2\sqrt{3}}}=\frac{2+\sqrt{3}}{2+\sqrt{3}+1}+\frac{2-\sqrt{3}}{2-\left(\sqrt{3}-1\right)}\\ =\frac{2+\sqrt{3}}{3+\sqrt{3}}+\frac{2-\sqrt{3}}{3-\sqrt{3}}=\frac{\left(2+\sqrt{3}\right)\left(3-\sqrt{3}\right)+\left(2-\sqrt{3}\right)\left(3+\sqrt{3}\right)}{9-3}\\ =\frac{6-3+\sqrt{3}+6-3-\sqrt{3}}{6}=\frac{6}{6}=1\end{array}$

https://khoahoc.vietjack.com/question/1009088

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mfrac><mrow><mn>1</mn><mo>+</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></mrow><mrow><mn>1</mn><mo>+</mo><msqrt><mn>1</mn><mo>+</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></msqrt></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>1</mn><mo>−</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></mrow><mrow><mn>1</mn><mo>−</mo><msqrt><mn>1</mn><mo>−</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></msqrt></mrow></mfrac></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mtext> </mtext><mi>G</mi><mo>=</mo><mfrac><mrow><mn>1</mn><mo>+</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></mrow><mrow><mn>1</mn><mo>+</mo><msqrt><mn>1</mn><mo>+</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></msqrt></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>1</mn><mo>−</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></mrow><mrow><mn>1</mn><mo>−</mo><msqrt><mn>1</mn><mo>−</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></msqrt></mrow></mfrac><mo>=</mo><mfrac><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mn>2</mn></mfrac><mfrac><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></msqrt></mrow><msqrt><mn>2</mn></msqrt></mfrac></mfrac><mo>+</mo><mfrac><mfrac><mrow><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow><mn>2</mn></mfrac><mfrac><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><msqrt><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></msqrt></mrow><msqrt><mn>2</mn></msqrt></mfrac></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mn>2</mn></mfrac><mo>.</mo><mfrac><msqrt><mn>2</mn></msqrt><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></msqrt></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow><mn>2</mn></mfrac><mo>.</mo><mfrac><msqrt><mn>2</mn></msqrt><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><msqrt><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></msqrt></mrow></mfrac></mtd></mtr></mtable></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mo>=</mo><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><msqrt><mn>2</mn></msqrt><mo>.</mo><mfenced><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></msqrt></mrow></mfenced></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><msqrt><mn>2</mn></msqrt><mo>.</mo><mfenced><mrow><msqrt><mn>2</mn></msqrt><mo>−</mo><msqrt><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></msqrt></mrow></mfenced></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn><mo>+</mo><msqrt><mn>4</mn><mo>+</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></msqrt></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn><mo>−</mo><msqrt><mn>4</mn><mo>−</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn><mo>−</mo><mfenced><mrow><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>3</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>3</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfrac><mo>=</mo><mfrac><mrow><mfenced><mrow><mn>2</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mfenced><mrow><mn>3</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mo>+</mo><mfenced><mrow><mn>2</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced><mfenced><mrow><mn>3</mn><mo>+</mo><msqrt><mn>3</mn></msqrt></mrow></mfenced></mrow><mrow><mn>9</mn><mo>−</mo><mn>3</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow><mn>6</mn><mo>−</mo><mn>3</mn><mo>+</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>6</mn><mo>−</mo><mn>3</mn><mo>−</mo><msqrt><mn>3</mn></msqrt></mrow><mn>6</mn></mfrac><mo>=</mo><mfrac><mn>6</mn><mn>6</mn></mfrac><mo>=</mo><mn>1</mn></mtd></mtr></mtable></math>

Free Form

Lớp 9

Rút gọn biểu thức : $ 2\sqrt{27}-\sqrt{\frac{16}{3}}-\sqrt{48}-\sqrt{8\frac{1}{3}}$

$ \begin{array}{l}2\sqrt{27}-\sqrt{\frac{16}{3}}-\sqrt{48}-\sqrt{8\frac{1}{3}}\\ =2\sqrt{9.3}-\frac{\sqrt{16}}{\sqrt{3}}-\sqrt{16.3}-\frac{\sqrt{25}}{\sqrt{3}}\\ =2.3\sqrt{3}-\frac{4}{\sqrt{3}}-4\sqrt{3}-\frac{5}{\sqrt{3}}\\ =6\sqrt{3}-\frac{4}{3}\sqrt{3}-4\sqrt{3}-\frac{5}{3}\sqrt{3}=-\sqrt{3}\end{array}$

https://khoahoc.vietjack.com/question/1009093

### Câu hỏi: Rút gọn biểu thức : <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msqrt><mn>27</mn></msqrt><mo>−</mo><msqrt><mfrac><mn>16</mn><mn>3</mn></mfrac></msqrt><mo>−</mo><msqrt><mn>48</mn></msqrt><mo>−</mo><msqrt><mn>8</mn><mfrac><mn>1</mn><mn>3</mn></mfrac></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mn>2</mn><msqrt><mn>27</mn></msqrt><mo>−</mo><msqrt><mfrac><mn>16</mn><mn>3</mn></mfrac></msqrt><mo>−</mo><msqrt><mn>48</mn></msqrt><mo>−</mo><msqrt><mn>8</mn><mfrac><mn>1</mn><mn>3</mn></mfrac></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mn>2</mn><msqrt><mn>9.3</mn></msqrt><mo>−</mo><mfrac><msqrt><mn>16</mn></msqrt><msqrt><mn>3</mn></msqrt></mfrac><mo>−</mo><msqrt><mn>16.3</mn></msqrt><mo>−</mo><mfrac><msqrt><mn>25</mn></msqrt><msqrt><mn>3</mn></msqrt></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mn>2.3</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mfrac><mn>4</mn><msqrt><mn>3</mn></msqrt></mfrac><mo>−</mo><mn>4</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mfrac><mn>5</mn><msqrt><mn>3</mn></msqrt></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mn>6</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>4</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mfrac><mn>5</mn><mn>3</mn></mfrac><msqrt><mn>3</mn></msqrt><mo>=</mo><mo>−</mo><msqrt><mn>3</mn></msqrt></mtd></mtr></mtable></math>

Free Form

Lớp 9

$ \left(\sqrt{125}-\sqrt{12}-2\sqrt{5}\right)\left(3\sqrt{5}-\sqrt{3}+\sqrt{27}\right)$

$ \begin{array}{l}\left(\sqrt{125}-\sqrt{12}-2\sqrt{5}\right)\left(3\sqrt{5}-\sqrt{3}+\sqrt{27}\right)\\ =\left(5\sqrt{5}-2\sqrt{3}-2\sqrt{5}\right)\left(3\sqrt{5}-\sqrt{3}+3\sqrt{3}\right)\\ =\left(3\sqrt{5}-2\sqrt{3}\right)\left(3\sqrt{5}+2\sqrt{3}\right)\\ ={\left(3\sqrt{5}\right)}^{2}-{\left(2\sqrt{3}\right)}^{2}=45-12=33\end{array}$

https://khoahoc.vietjack.com/question/1009096

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msqrt><mn>125</mn></msqrt><mo>−</mo><msqrt><mn>12</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><mn>3</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><msqrt><mn>27</mn></msqrt></mrow></mfenced></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfenced><mrow><msqrt><mn>125</mn></msqrt><mo>−</mo><msqrt><mn>12</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><mn>3</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><msqrt><mn>27</mn></msqrt></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mn>5</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>3</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>5</mn></msqrt></mrow></mfenced><mfenced><mrow><mn>3</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><mn>3</mn><msqrt><mn>3</mn></msqrt></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mn>3</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></mrow></mfenced><mfenced><mrow><mn>3</mn><msqrt><mn>5</mn></msqrt><mo>+</mo><mn>2</mn><msqrt><mn>3</mn></msqrt></mrow></mfenced></mtd></mtr><mtr><mtd><mo>=</mo><msup><mfenced><mrow><mn>3</mn><msqrt><mn>5</mn></msqrt></mrow></mfenced><mn>2</mn></msup><mo>−</mo><msup><mfenced><mrow><mn>2</mn><msqrt><mn>3</mn></msqrt></mrow></mfenced><mn>2</mn></msup><mo>=</mo><mn>45</mn><mo>−</mo><mn>12</mn><mo>=</mo><mn>33</mn></mtd></mtr></mtable></math>

Free Form

Lớp 9

$ \left(3\sqrt{20}-\sqrt{125}-15\sqrt{\frac{1}{5}}\right).\sqrt{5}$

$ \begin{array}{l}\left(3\sqrt{20}-\sqrt{125}-15\sqrt{\frac{1}{5}}\right).\sqrt{5}\\ =\left(3\sqrt{4.5}-\sqrt{25.5}-\frac{15}{\sqrt{5}}\right).\sqrt{5}\\ =\left(6\sqrt{5}-5\sqrt{5}-\frac{15}{\sqrt{5}}\right).\sqrt{5}\\ =\sqrt{5}.\sqrt{5}-\text{\hspace{0.17em}}\frac{15}{\sqrt{5}}.\sqrt{5}=5-15=-10\end{array}$

https://khoahoc.vietjack.com/question/1009101

### Câu hỏi: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>3</mn><msqrt><mn>20</mn></msqrt><mo>−</mo><msqrt><mn>125</mn></msqrt><mo>−</mo><mn>15</mn><msqrt><mfrac><mn>1</mn><mn>5</mn></mfrac></msqrt></mrow></mfenced><mo>.</mo><msqrt><mn>5</mn></msqrt></math> ### Lời giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mfenced><mrow><mn>3</mn><msqrt><mn>20</mn></msqrt><mo>−</mo><msqrt><mn>125</mn></msqrt><mo>−</mo><mn>15</mn><msqrt><mfrac><mn>1</mn><mn>5</mn></mfrac></msqrt></mrow></mfenced><mo>.</mo><msqrt><mn>5</mn></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mn>3</mn><msqrt><mn>4.5</mn></msqrt><mo>−</mo><msqrt><mn>25.5</mn></msqrt><mo>−</mo><mfrac><mn>15</mn><msqrt><mn>5</mn></msqrt></mfrac></mrow></mfenced><mo>.</mo><msqrt><mn>5</mn></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><mfenced><mrow><mn>6</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mn>5</mn><msqrt><mn>5</mn></msqrt><mo>−</mo><mfrac><mn>15</mn><msqrt><mn>5</mn></msqrt></mfrac></mrow></mfenced><mo>.</mo><msqrt><mn>5</mn></msqrt></mtd></mtr><mtr><mtd><mo>=</mo><msqrt><mn>5</mn></msqrt><mo>.</mo><msqrt><mn>5</mn></msqrt><mo>−</mo><mtext> </mtext><mfrac><mn>15</mn><msqrt><mn>5</mn></msqrt></mfrac><mo>.</mo><msqrt><mn>5</mn></msqrt><mo>=</mo><mn>5</mn><mo>−</mo><mn>15</mn><mo>=</mo><mo>−</mo><mn>10</mn></mtd></mtr></mtable></math>