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 `

Đáp án:

`a)3sqrt352-2sqrt63-2sqrt28-1/5sqrt175`

`=3sqrt{36.7}-2sqrt{9.7}-2sqrt{4.7}-1/5sqrt{25.7}`

`=18sqrt7-6sqrt7-4sqrt7-sqrt7`

`=7sqrt7`

`b)sqrt{69-28sqrt5}-sqrt{45-20sqrt5}`

`=sqrt{20-2.2sqrt5.7+49}-sqrt{5(9-4sqrt5)}`

`=sqrt{(2sqrt5-7)^2}-sqrt{5(sqrt5-2)^2}`

`=|2sqrt5-7|-|sqrt5(sqrt5-2)|`

`=7-2sqrt5-5+2sqrt5`

`=2`

`c)(2sqrt5-5sqrt2)/(sqrt5-sqrt2)+15sqrt{2/5}-12/(sqrt10+2)`

`=(sqrt10(sqrt2-sqrt5))/(sqrt5-sqrt2)+3*(5sqrt2)/sqrt5-(12(sqrt10-2))/(10-4)`

`=-sqrt10+3sqrt10-2(sqrt10-2)`

`=4`