$\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}$

Đáp án:

`sqrt{13+30sqrt{2+sqrt{9+4sqrt{2}}}}=5+3sqrt{2}`

Giải thích các bước giải:

`sqrt{13+30sqrt{2+sqrt{9+4sqrt{2}}}`
`=sqrt{13+30sqrt{2+sqrt{9+2.2sqrt{2}.1}}}`
`=sqrt{13+30sqrt{2+sqrt{(2sqrt{2})^2+2.2sqrt{2}.1+1^2}}}`
`=sqrt{13+30sqrt{2+sqrt{(2sqrt{2}+1)^2}}}`
`=sqrt{13+30sqrt{2+|2sqrt{2}+1|}}`
`=sqrt{13+30sqrt{2+2sqrt{2}+1}}`
`=sqrt{13+30sqrt{3+2.sqrt{2}}`
`=sqrt{13+30sqrt{(sqrt{2})^2+2.sqrt{2}.1+1^2}}`
`=sqrt{13+30.sqrt{(sqrt{2}+1)^2}}`
`=sqrt{13+30.|sqrt{2}+1|}`
`=sqrt{13+30.(sqrt{2}+1)}`
`=sqrt{13+30sqrt{2}+30}`
`=sqrt{43+30sqrt{2}}`
`=sqrt{43+2.5.3sqrt{2}}`
`=sqrt{5^2+2.5.3sqrt{2}+(3sqrt{2})^2}`
`=sqrt{(5+3sqrt{2})^2}`
`=|5+3sqrt{2}|`
`=5+3sqrt{2}`