Đáp án + Giải thích các bước giải:
Câu 10.
`\frac{3sqrt2-2sqrt3}{sqrt3-sqrt2}-\frac{10}{1+sqrt6}`
`=\frac{sqrt2.sqrt3(sqrt3-sqrt2)(sqrt3+sqrt2)}{3-2}-\frac{10(1-sqrt6)}{1-6}`
`=sqrt6(3-2)+\frac{10(1-sqrt6)}{5}`
`=sqrt6+2(1-sqrt6)`
`=sqrt6+2-2sqrt6`
`=2-sqrt6`
Câu 16.
`sqrt(13-4sqrt3)-sqrt(2/(2+sqrt3))`
`=sqrt((2sqrt3-1)^2)-sqrt\frac{2(2-sqrt3)}{4-3}`
`=2sqrt3-1-sqrt{2(2-sqrt3)`
`=2sqrt3-1-sqrt{4-2sqrt3)`
`=2sqrt3-1-sqrt{(sqrt3-1)^2)`
`=2sqrt3-1-sqrt3+1`
`=sqrt3`
Câu 17:
`\frac{sqrt(9-4sqrt5)}{sqrt(sqrt5-2)}.sqrt(sqrt5+2)`
`=\frac{sqrt((sqrt5-2)^2)}{sqrt(sqrt5-2)}.sqrt(sqrt5+2)`
`=\frac{sqrt5-2}{sqrt(sqrt5-2)}.sqrt(sqrt5+2)`
`=sqrt(sqrt5-2).sqrt(sqrt5+2)`
`=sqrt((sqrt5-2)(sqrt5+2))`
`=sqrt(5-4)=1`
Câu 19:
`\frac{3+sqrt2}{2sqrt2-1}-sqrt((1+sqrt2)/(sqrt2-1))`
`=\frac{(3+sqrt2)(2sqrt2+1)}{(2sqrt2)^2-1^2}-sqrt((1+sqrt2)^2)`
`=\frac{(3+sqrt2)(2sqrt2+1)}{(2sqrt2)^2-1^2}-sqrt((1+sqrt2)^2)`
`=\frac{7+7sqrt2}{7}-|1+sqrt2|`
`=1+sqrt2-1-sqrt2`
`=0`
Câu 20:
`sqrt(16+4sqrt15)-sqrt(8-4sqrt3)-sqrt(3-sqrt5)`
`=sqrt(2(8+2sqrt15))-sqrt(2(4-2sqrt3))-sqrt(3-sqrt5)`
`=sqrt(2(sqrt5+sqrt3)^2)-sqrt(2(sqrt3-1)^2)-sqrt((6-2sqrt5)/2)`
`=sqrt2(sqrt5+sqrt3)-sqrt2(sqrt3-1)-sqrt(((sqrt5-1)^2)/2)`
`=sqrt10+sqrt6-sqrt6+sqrt2-(sqrt5-1)/sqrt2`
`=sqrt10+sqrt2-(sqrt5-1)/sqrt2`
`=\frac{2sqrt5+2-sqrt5+1}{sqrt2}`
`=\frac{sqrt5+3}{sqrt2}`
`=\frac{sqrt10+3sqrt2}{2}`
