a)Ta có:
`11+6sqrt{2}`
`=9+2.3sqrt{2}+2`
`=(3+sqrt{2})^2`
Mà `(3+sqrt{2})^2=(3+sqrt{2})^2`
Vậy `11+6sqrt{2}=(3+sqrt{2})^2`
b)Ta có:
`8-2sqrt{7}`
`=7-2sqrt{7}+1`
`=(sqrt{7}-1)^2`
Mà `(sqrt{7}-1)^2=(sqrt{7}-1)^2`
Vậy `8-2sqrt{7}=(sqrt{7}-1)^2`
c)Ta có:
`sqrt{11+6sqrt{2}}+sqrt{11-6sqrt{2}}`
`=sqrt{9+2.3sqrt{2}+2}+sqrt{9-2.3sqrt{2}+2}`
`=(3+sqrt{2})^2+(3-sqrt{2})^2`
`=|3+sqrt{2}|+|3-sqrt{2}|`
`=3+sqrt{2}+3-sqrt{2}`
`=6`
Mà `6=6`
Vậy `sqrt{11+6sqrt{2}}+sqrt{11-6sqrt{2}}=6`
`d)sqrt{8-2sqrt{7}}-sqrt{8+2sqrt{7}}`
`=sqrt{7-2sqrt{7}+1}-sqrt{7+2sqrt{7}+1}`
`=sqrt{(sqrt{7}-1)^2}-sqrt{(sqrt{7}+1})^2}`
`=|sqrt{7}-1|-|sqrt{7}+1|`
`=sqrt{7}-1-sqrt{7}-1`
`=-2`
Mà `-2=-2`
Vậy `sqrt{8-2sqrt{7}}-sqrt{8+2sqrt{7}}=-2.`
