Đáp án + Giải thích các bước giải:
`16.` `(sqrt5+1)/(2sqrt5-4)`
`=(sqrt5+1)/[2(sqrt5-2)]`
`=[(sqrt5+1)(sqrt5+2)]/[2(sqrt5-2)(sqrt5+2)]`
`=[(sqrt5+1)(sqrt5+2)]/[2(5-4)]`
`=[(sqrt5+1)(sqrt5+2)]/2`
`=(5+2sqrt5+sqrt5+2)/2`
`=(7+3sqrt5)/2`
`17.`
`12/(3-sqrt3)=[12(3+sqrt3)]/[(3-sqrt3)(3+sqrt3)]`
`=[12(3+sqrt3)]/(9-3)`
`=[12(3+sqrt3)]/6=2(3+sqrt3)=6+2sqrt3`
`18.`
`(3sqrt5)/(2sqrt5-1)=[3sqrt5(2sqrt5+1)]/[(2sqrt5-1)(2sqrt5+1)]`
`=(6*5+3sqrt5)/[(2sqrt5)^2-1]`
`=(30+3sqrt5)/(20-1)=(30+3sqrt5)/19`
`19.` `3/(2sqrt2-sqrt5)`
`=[3(2sqrt2+sqrt5)]/[(2sqrt2-sqrt5)(2sqrt2+sqrt5)]`
`=(6sqrt2+3sqrt5)/[(2sqrt2)^2-(sqrt5)^2]`
`=(6sqrt2+15)/(8-5)`
`=(6sqrt2+15)/3`
`=[3(2sqrt2+5)]/3`
`=2sqrt2+5`
`20.` `(sqrt5+sqrt3)/(sqrt5-sqrt3)`
`=[(sqrt5+sqrt3)(sqrt5+sqrt3)]/[(sqrt5-sqrt3)(sqrt5+sqrt3)]`
`=(5+sqrt15+sqrt15+3)/(5-3)`
`=(8+2sqrt15)/2`
`=[2(4+sqrt15)]/2=4+sqrt15`.
