12) \(\sqrt{2+\sqrt{9+\sqrt{32}}}\)

\(\sqrt{32}=4\sqrt2\), и \(9+4\sqrt2=(1+2\sqrt2)^2\). Значит, \(\sqrt{9+\sqrt{32}}=1+2\sqrt2\), а \(2+(1+2\sqrt2)=3+2\sqrt2=(1+\sqrt2)^2\).

Ответ: \(1+\sqrt2\).