Đáp án :
`1)` `19\sqrt3 + 22\sqrt2`
`2)` `-3\sqrt5`
`3)` `5 - \sqrt6`
Giải thích các bước giải :
`1)` `3\sqrt75 - 3\sqrt32 + \sqrt48 - \sqrt200`
`= 3. \sqrt{ 25 . 3 } - 3. \sqrt{16.2} + \sqrt{ 16.3} - \sqrt{100.2} `
`= 3. 5\sqrt3 - 3. 4\sqrt2 + 4\sqrt3 - 10\sqrt2`
`= 15\sqrt3 - 12sqrt2 + 4\sqrt3 - 10\sqrt2`
`= 19\sqrt3 + 22\sqrt2`
`2)` `2\sqrt20 - \frac{5}{6}\sqrt180 - \sqrt125 + \sqrt45`
`= 2. \sqrt{4.5} - \frac{5}{6}.\sqrt{ 36.5} - \sqrt{ 25.5} + \sqrt{ 9.5}`
`= 2. 2\sqrt5 - \frac{5}{6}.6\sqrt5 - 5\sqrt5 + 3\sqrt5`
`= 4\sqrt5 - 5\sqrt5 - 5\sqrt5 + 3\sqrt5`
`= -3\sqrt5`
`3)` `\sqrt{( \sqrt5 - 3 )^2} + \sqrt{ 9 + 4\sqrt5 } + \frac{3\sqrt2 - 2\sqrt3}{\sqrt2 - \sqrt3}`
`= | \sqrt5 - 3 | + \sqrt{4 + 4\sqrt5 + 5}+ \frac{ \sqrt2 ( 3\sqrt2 - 2\sqrt3 )}{\sqrt2 ( \sqrt2 - \sqrt3 )}`
`= 3 - \sqrt5 + \sqrt{2^2 + 2.2.\sqrt5 + ( \sqrt5 )^2} + \frac{6 - 2\sqrt6}{2 - \sqrt6}`
`= 3 - \sqrt5 + sqrt{ (2 + \sqrt5 )^2} + \frac{ - ( 6 + 2\sqrt6 ) }{- ( 2 - \sqrt6) }`
`= 3 - \sqrt5 + | 2 + \sqrt5 | + \frac{-\sqrt6 (\sqrt6 - 2 ) }{- 2 + \sqrt6}`
`= 3 - \sqrt5 + 2 + \sqrt5 - \sqrt6`
`= 5 - \sqrt6`
