Question

$17+12\sqrt{2}$

Answer 1

$$\begin{gathered} \sqrt{17+12\sqrt{2}} \\ =\sqrt{17+12\sqrt{2}} \\ =\sqrt{\left(8+9\right)+2\times 2\sqrt{2}\times 3} \\ =\sqrt{{\left(2\sqrt{2}\right)}^2+{\left(3\right)}^2+2\times 2\sqrt{2}\times 3} \\ =\sqrt{{\left(2\sqrt{2}+3\right)}^2} \\ =2\sqrt{2}+3 \end{gathered}$$