Answer: ## Bài tập 2. Trục căn thức ở mẫu:

**a)**

* $\frac{1}{\sqrt{2}} = \frac{1\cdot \sqrt{2}}{\sqrt{2}\cdot \sqrt{2}} = \frac{\sqrt{2}}{2}$ †Answer: 
* $\frac{1}{3\sqrt{2}} = \frac{1\cdot \sqrt{2}}{3\sqrt{2}\cdot \sqrt{2}} = \frac{\sqrt{2}}{6}$ †Answer: 
* $\frac{12}{5\sqrt{2}} = \frac{12\cdot \sqrt{2}}{5\sqrt{2}\cdot \sqrt{2}} = \frac{12\sqrt{2}}{10} = \frac{6\sqrt{2}}{5}$ †Answer: 
* $\frac{12}{\sqrt{5}-1} = \frac{12(\sqrt{5}+1)}{(\sqrt{5}-1)(\sqrt{5}+1)} = \frac{12(\sqrt{5}+1)}{5-1} = 3(\sqrt{5}+1)$ †Answer: 

**b)**

* $\frac{2}{\sqrt{5}+1} = \frac{2(\sqrt{5}-1)}{(\sqrt{5}+1)(\sqrt{5}-1)} = \frac{2(\sqrt{5}-1)}{5-1} = \frac{\sqrt{5}-1}{2}$ †Answer: 
* $\frac{3}{\sqrt{5}} = \frac{3\cdot \sqrt{5}}{\sqrt{5}\cdot \sqrt{5}} = \frac{3\sqrt{5}}{5}$ †Answer: 
* $\frac{3}{2\sqrt{5}} = \frac{3\cdot \sqrt{5}}{2\sqrt{5}\cdot \sqrt{5}} = \frac{3\sqrt{5}}{10}$ †Answer: 
* $\frac{31}{3\sqrt{5}} = \frac{31\cdot \sqrt{5}}{3\sqrt{5}\cdot \sqrt{5}} = \frac{31\sqrt{5}}{15}$ †Answer: 

**c)**

* $\frac{3+\sqrt{2}}{2+\sqrt{6}} = \frac{(3+\sqrt{2})(2-\sqrt{6})}{(2+\sqrt{6})(2-\sqrt{6})} = \frac{6-3\sqrt{6}+2\sqrt{2}-\sqrt{12}}{4-6} = \frac{6-3\sqrt{6}+2\sqrt{2}-2\sqrt{3}}{-2} = -3 + \frac{3\sqrt{6}}{2} - \sqrt{2} + \sqrt{3}$ †Answer: 
* $\frac{3+\sqrt{2}}{2+3\sqrt{6}} = \frac{(3+\sqrt{2})(2-3\sqrt{6})}{(2+3\sqrt{6})(2-3\sqrt{6})} = \frac{6-9\sqrt{6}+2\sqrt{2}-3\sqrt{12}}{4-54} = \frac{6-9\sqrt{6}+2\sqrt{2}-6\sqrt{3}}{-50} = -\frac{3}{25} + \frac{9\sqrt{6}}{50} - \frac{\sqrt{2}}{25} + \frac{3\sqrt{3}}{25}$ †Answer: 
* $\frac{4}{\sqrt{6}} = \frac{4\cdot \sqrt{6}}{\sqrt{6}\cdot \sqrt{6}} = \frac{4\sqrt{6}}{6} = \frac{2\sqrt{6}}{3}$ †Answer: 
* $\frac{4}{3\sqrt{6}} = \frac{4\cdot \sqrt{6}}{3\sqrt{6}\cdot \sqrt{6}} = \frac{4\sqrt{6}}{18} = \frac{2\sqrt{6}}{9}$ †Answer: 

**d)**

* $\frac{4}{15\sqrt{6}} = \frac{4\cdot \sqrt{6}}{15\sqrt{6}\cdot \sqrt{6}} = \frac{4\sqrt{6}}{90} = \frac{2\sqrt{6}}{45}$ †Answer: 
* $\frac{3}{2\sqrt{3}-3\sqrt{2}} = \frac{3(2\sqrt{3}+3\sqrt{2})}{(2\sqrt{3}-3\sqrt{2})(2\sqrt{3}+3\sqrt{2})} = \frac{6\sqrt{3}+9\sqrt{2}}{12-18} = -\frac{6\sqrt{3}+9\sqrt{2}}{6} = -\sqrt{3} - \frac{3\sqrt{2}}{2}$ †Answer: 
* $\frac{1}{2\sqrt{3}-\sqrt{2}} = \frac{2\sqrt{3}+\sqrt{2}}{(2\sqrt{3}-\sqrt{2})(2\sqrt{3}+\sqrt{2})} = \frac{2\sqrt{3}+\sqrt{2}}{12-2} = \frac{2\sqrt{3}+\sqrt{2}}{10}$ †Answer: 
* $\frac{3}{\sqrt{15}} = \frac{3\cdot \sqrt{15}}{\sqrt{15}\cdot \sqrt{15}} = \frac{3\sqrt{15}}{15} = \frac{\sqrt{15}}{5}$ †Answer: 

**e)**

* $\frac{3}{2\sqrt{15}} = \frac{3\cdot \sqrt{15}}{2\sqrt{15}\cdot \sqrt{15}} = \frac{3\sqrt{15}}{30} = \frac{\sqrt{15}}{10}$ †Answer: 
* $\frac{3-\sqrt{2}}{6\sqrt{15}} = \frac{(3-\sqrt{2})\cdot \sqrt{15}}{6\sqrt{15}\cdot \sqrt{15}} = \frac{3\sqrt{15}-\sqrt{30}}{90} = \frac{\sqrt{15}-\sqrt{30}}{30}$ †Answer: 
* $\frac{5}{\sqrt{2}+1} = \frac{5(\sqrt{2}-1)}{(\sqrt{2}+1)(\sqrt{2}-1)} = \frac{5(\sqrt{2}-1)}{2-1} = 5(\sqrt{2}-1)$ †Answer: 
* $\frac{3}{\sqrt{2}+1} = \frac{3(\sqrt{2}-1)}{(\sqrt{2}+1)(\sqrt{2}-1)} = \frac{3(\sqrt{2}-1)}{2-1} = 3(\sqrt{2}-1)$ †Answer: 

**f)**

* $\frac{12}{3-\sqrt{3}} = \frac{12(3+\sqrt{3})}{(3-\sqrt{3})(3+\sqrt{3})} = \frac{12(3+\sqrt{3})}{9-3} = 2(3+\sqrt{3})$ †Answer: 
* $\frac{7\sqrt{3}-5\sqrt{11}}{8\sqrt{3}-7\sqrt{11}} = \frac{(7\sqrt{3}-5\sqrt{11})(8\sqrt{3}+7\sqrt{11})}{(8\sqrt{3}-7\sqrt{11})(8\sqrt{3}+7\sqrt{11})} = \frac{168+49\sqrt{33}-40\sqrt{33}-385}{192-77} = \frac{-217+9\sqrt{33}}{115}$ †Answer: 
* $\frac{3\sqrt{5}-2\sqrt{2}}{2\sqrt{5}-3\sqrt{2}} = \frac{(3\sqrt{5}-2\sqrt{2})(2\sqrt{5}+3\sqrt{2})}{(2\sqrt{5}-3\sqrt{2})(2\sqrt{5}+3\sqrt{2})} = \frac{30+9\sqrt{10}-4\sqrt{10}-12}{20-18} = \frac{18+5\sqrt{10}}{2}$ †Answer: 
* $\frac{2}{3+\sqrt{3}} = \frac{2(3-\sqrt{3})}{(3+\sqrt{3})(3-\sqrt{3})} = \frac{2(3-\sqrt{3})}{9-3} = \frac{3-\sqrt{3}}{3}$ †Answer: 

**g)**

* $\frac{7\sqrt{3}-\sqrt{11}}{8\sqrt{3}-\sqrt{11}} = \frac{(7\sqrt{3}-\sqrt{11})(8\sqrt{3}+\sqrt{11})}{(8\sqrt{3}-\sqrt{11})(8\sqrt{3}+\sqrt{11})}$ †Answer: