Đáp án:
`a)` `7\sqrt7`
`b)` `2`
`c)` `4`
Giải thích các bước giải:
`a)` `3\sqrt{252} - 2\sqrt{63} - 2\sqrt28 - \frac{1}{5}\sqrt175`
`= 3\sqrt{36.7} - 2\sqrt{9.7} - 2\sqrt{4.7} - \frac{1}{5}\sqrt{25.7}`
`= 3. 6\sqrt7 - 2.3\sqrt7 - 2.2\sqrt7 - \frac{1}{5}.5\sqrt7`
`= 18\sqrt7 - 6\sqrt7 - 4\sqrt7 - \sqrt7`
`= ( 18 - 6 - 4 - 1 ).\sqrt7`
`= 7\sqrt7`
`b)` `\sqrt{69-28\sqrt5} - \sqrt{45-20\sqrt5}`
`= \sqrt{49 - 28\sqrt5 + 20} - \sqrt{25 - 20\sqrt5 + 20}`
`= \sqrt{7^2 - 2 . 7 . 2\sqrt5 + ( 2\sqrt5 )^2} - \sqrt{5^2 - 2 . 5 . 2\sqrt5 + (2\sqrt5)^2}`
`= \sqrt{( 7 - 2\sqrt5 )^2} - \sqrt{(5-2\sqrt5)^2}`
`= | 7 - 2\sqrt5 | - | 5 - 2\sqrt5 |`
`= 7-2\sqrt5 -5 + 2\sqrt5`
`= 2`
`c)` `\frac{2\sqrt5 - 5\sqrt2}{\sqrt5 - \sqrt2} + 15\sqrt\frac{2}{5} - \frac{12}{\sqrt10 + 2 }`
`= \frac{\sqrt2( 2\sqrt5 - 5\sqrt2 )}{\sqrt2 ( \sqrt5 - \sqrt2 )}+ 15 .\frac{\sqrt10}{5} - \frac{12}{\sqrt10 +2}`
`= \frac{2\sqrt10 -10}{\sqrt10 - 2}+ 15 . \frac{\sqrt10}{5}- \frac{12}{\sqrt10 + 2}`
`= \frac{- ( 2\sqrt10 - 10 )}{- ( \sqrt10 - 2 )} +\frac{15\sqrt10}{5} - \frac{12}{\sqrt10 + 2}`
`= \frac{-2\sqrt10 + 10}{-\sqrt10 + 2}+3\sqrt10-\frac{12}{\sqrt10 + 2 }`
`= \frac{-\sqrt10 ( 2 - \sqrt10 )}{-\sqrt10 + 2} +3\sqrt10 - ( - 4 + 2\sqrt10 )`
`= -\sqrt10 + 3\sqrt10+4-2\sqrt10`
`= ( -1 + 3 - 2 ) . \sqrt10 + 4`
`= 4 `
