Đáp án + Giải thích các bước giải:
`11.` `12/(2sqrt7-5)=[12(2sqrt7+5)]/[(2sqrt7-5)(2sqrt7+5)]`
`=[12(2sqrt7+5)]/[(2sqrt7)^2-5^2]`
`=[12(2sqrt7+5)]/(28-25)`
`=[12(2sqrt7+5)]/3=4(2sqrt7+5)`
`12.` `(8-3sqrt3)/(7+2sqrt3)`
`=[(8-3sqrt3)(7-2sqrt3)]/[(7-2sqrt3)(7+2sqrt3)]`
`=(56-16sqrt3-21sqrt3+18)/(49-12)`
`=(74-37sqrt3)/37`
`=[37(2-sqrt3)]/37=2-sqrt3`
`13.` `(9-4sqrt5)/(2-sqrt5)`
`=[(9-4sqrt5)(2+sqrt5)]/[(2-sqrt5)(2+sqrt5)]`
`=(18+9sqrt5-8sqrt5-20)/(4-5)`
`=(sqrt5-2)/(-1)=(-(sqrt5-2))/1=2-sqrt5`
`14.` `(3+2sqrt2)/(sqrt2+1)`
`=[(3+2sqrt2)(sqrt2-1)]/[(sqrt2-1)(sqrt2+1)]`
`=(3sqrt2-3+4-2sqrt2)/(2-1)`
`=(sqrt2+1)/1=sqrt2+1`
`15.` `(8-4sqrt3)/(1-sqrt3)`
`=[(8-4sqrt3)(1+sqrt3)]/[(1-sqrt3)(1+sqrt3)]`
`=(8+8sqrt3-4sqrt3-12)/(1-3)`
`=(4sqrt3-4)/(-2)`
`=[4(sqrt3-1)]/(-2)=-2(sqrt3-1)`
`=2-2sqrt3`
`16.` `(2sqrt3-6)/(sqrt3-1)`
`=[(2sqrt3-6)(sqrt3+1)]/[(sqrt3-1)(sqrt3+1)]`
`=(6+2sqrt3-6sqrt3-6)/(3-1)`
`=(-4sqrt3)/2=-2sqrt3`
`17.` `(2sqrt2-8)/(4-sqrt2)`
`=[(2sqrt2-8)(4+sqrt2)]/[(4-sqrt2)(4+sqrt2)]`
`=(8sqrt2+4-32-8sqrt2)/(16-2)`
`=(-28)/14=-2`
`18.`
`(9+3sqrt3)/(3sqrt3+3)`
`=[3(3+sqrt3)]/[3(sqrt3+1)]`
`=(3+sqrt3)/(sqrt3+1)`
`=[(3+sqrt3)(sqrt3-1)]/[(sqrt3-1)(sqrt3+1)]`
`=(3sqrt3-3+3-sqrt3)/(3-1)`
`=(2sqrt3)/2=sqrt3`.
