Đáp án:
`\sqrt{17+12\sqrt2}`
`=\sqrt{9+2.3.2sqrt2+8}`
`=sqrt{(3+2sqrt2)^2}=3+2sqrt2` $\\$
`(\sqrt2-sqrt{11+6sqrt2})/(sqrt{6+2sqrt5}-sqrt5)`
`=(sqrt2-sqrt{9+2.3sqrt2+2})/(sqrt{5+2sqrt5+1}-sqrt5)`
`=(sqrt2-sqrt{(3+sqrt2)^2})/(sqrt{(sqrt5+1)^2}-sqrt5)`
`=(sqrt2-3-sqrt2)/(sqrt5+1-sqrt5)=-3`
`sqrt{6+2sqrt{4-2sqrt3}}`
`=sqrt{6+2sqrt{3-2sqrt3+1}}`
`=sqrt{6+2sqrt{(sqrt3-1)^2}}`
`=sqrt{6+2(sqrt3-1)}`
`=sqrt{6+2sqrt3-2}`
`=sqrt{4+2sqrt3}`
`=sqrt{3+2sqrt3+1}`
`=sqrt{(sqrt3+1)^2}=sqrt3+1`
