Đáp án: `8)` `1`
`9)` `0`
`10)`` sqrt(7,5)-sqrt(2,5)+sqrt3-1`
`2)` `-2`
Giải thích các bước giải:
`8) ``(sqrt(3-sqrt(5)).(3+sqrt5))/(sqrt10 + sqrt2)=(sqrt(3-sqrt(5)).sqrt(3+sqrt5).sqrt(3+sqrt5))/(sqrt10 + sqrt2)`
`=(sqrt((3-sqrt5)(3+sqrt5)).sqrt(3+sqrt5))/(sqrt10 + sqrt2)=(sqrt((3^2-sqrt5^2)).sqrt(3+sqrt5))/(sqrt10 + sqrt2)`
`=(sqrt((9-5)).sqrt(3+sqrt5))/(sqrt10 + sqrt2)=(sqrt(4).sqrt(3+sqrt5))/(sqrt10 + sqrt2)=(sqrt(12+4sqrt5))/(sqrt10 + sqrt2)`
`=(sqrt(10+2+2sqrt20))/(sqrt10 + sqrt2)=(sqrt(sqrt10^2+2sqrt(10.2)+sqrt2^2))/(sqrt10 + sqrt2)`
`=sqrt((sqrt10+sqrt20)^2)/(sqrt10 + sqrt2)=(sqrt10 + sqrt2)/(sqrt10 + sqrt2)=1`
.
`9)` `sqrt(8sqrt3)-2sqrt(25sqrt12)+4sqrtsqrt192=sqrt(8sqrt3)-2sqrt(25sqrt(4.3))+4sqrtsqrt(64.3)`
`=sqrt(8sqrt3)-2sqrt(25sqrt(2^(2).3))+4sqrtsqrt(8^(2).3)=sqrt(8sqrt3)-2sqrt(50sqrt(3))+4sqrt(8sqrt(3))`
`=(sqrt(8sqrt3)+4sqrt(8sqrt(3)))-2sqrt(50sqrt(3))=5sqrt(8sqrt3)-sqrt(2^(2).50sqrt(3))`
`=sqrt(5^(2).8sqrt3)-sqrt(2^(2).50sqrt(3))=sqrt(200sqrt3)-sqrt(200sqrt(3))=0`
.
`10)``sqrt(2-sqrt3)(sqrt5+sqrt2)=sqrt(2-sqrt3).sqrt5+sqrt(2-sqrt3).sqrt2`
`=sqrt(2.5-5sqrt3)+sqrt(2.2-2sqrt3)=sqrt(10-2.2,5sqrt3)+sqrt(4-2sqrt3)`
`=sqrt(7,5+2,5-2sqrt(2,5^(2).3))+sqrt(3+1-2sqrt3)`
`=sqrt(sqrt(7,5)^2-2sqrt(18,75)+sqrt(2,5)^2)+sqrt(sqrt3^2-2sqrt3.1+sqrt1^2)`
`=sqrt(sqrt(7,5)^2-2sqrt(7,5.2,5)+sqrt(2,5)^2)+sqrt(sqrt3-sqrt1)^2=sqrt(sqrt(7,5)-sqrt(2,5))^2+sqrt(sqrt3-1)^2`
`=sqrt(7,5)-sqrt(2,5)+sqrt3-1`
.
`2)``(10+2sqrt10)/(sqrt5+sqrt2)+8/(1-sqrt5)=(2.5+2sqrt5.2)/(sqrt5+sqrt2)+(10-2+2sqrt5-2sqrt5)/(1-sqrt5)`
`=(2.sqrt5.sqrt5+2sqrt5.sqrt2)/(sqrt5+sqrt2)+((-2+2sqrt5)+(10-2sqrt5))/(1-sqrt5)`
`=(2sqrt5.(sqrt5+sqrt2))/(sqrt5+sqrt2)+(-2(1-sqrt5)+(2.sqrt5.sqrt5-2sqrt5))/(1-sqrt5)`
`=2sqrt5+(-2(1-sqrt5)-2sqrt5(1-sqrt5))/(1-sqrt5)`
`=2sqrt5+((-2-2sqrt5)(1-sqrt5))/(1-sqrt5)`
`=2sqrt5+(-2-2sqrt5)=-2`
