Đáp án + Giải thích các bước giải:
`sqrt(6+2sqrt5)/(sqrt5+1)`
`=sqrt(5+2sqrt5+1)/(sqrt5+1)`
`=sqrt((sqrt5)^2+2*sqrt5*1+1^2)/(sqrt5+1)`
`=sqrt[(sqrt5+1)^2]/(sqrt5+1)=|sqrt5+1|/(sqrt5+1)`
`=(sqrt5+1)/(sqrt5+1)=1`
`sqrt(5-2sqrt6)/(sqrt3-sqrt2)`
`=sqrt(3-2sqrt6+2)/(sqrt3-sqrt2)`
`=sqrt(3-2*sqrt3*sqrt2+2)/(sqrt3-sqrt2)`
`=sqrt[(sqrt3)^2-2sqrt3*sqrt2+(sqrt2)^2]/(sqrt3-sqrt2)`
`=sqrt[(sqrt3-sqrt2)^2]/(sqrt3-sqrt2)`
`=|sqrt3-sqrt2|/(sqrt3-sqrt2)=(sqrt3-sqrt2)/(sqrt3-sqrt2)=1`
Vậy `sqrt(6+2sqrt5)/(sqrt5+1)=sqrt(5-2sqrt6)/(sqrt3-sqrt2)`
