`sqrt{4+sqrt8}.sqrt{2+sqrt{2+sqrt2}}.sqrt{2-sqrt{2+sqrt2}}`
`=\sqrt{4+2sqrt2}.sqrt{4-(2+sqrt2)}`
`=sqrt{4+2sqrt2}.sqrt{2-sqrt2}`
`=sqrt{(4+2sqrt2)(2-sqrt2)}`
`=sqrt{2(2+sqrt2)(2-sqrt2)}`
`=sqrt{2(4-2)}`
`=sqrt{2.2}`
`=2`
`sqrt{4+sqrt2}.sqrt{sqrt3+sqrt{sqrt2-1}}.sqrt{sqrt3-sqrt{sqrt2-1}}`
`=sqrt{4+sqrt2}.sqrt{sqrt3^2-sqrt{sqrt2-1}^2}`
`=sqrt{4+sqrt2}.sqrt{3-(sqrt2-1)}`
`=sqrt{4+sqrt2}.sqrt{4-sqrt2}`
`=sqrt{16-2}`
`=sqrt{14}`