$$
(\sqrt{2}-1) \cdot \sqrt[4]{17+12 \sqrt{2}}=?
$$


$$
\begin{aligned}
& (\sqrt{2}-1) \cdot \sqrt[4]{17+12 \sqrt{2}}=\sqrt[4]{(\sqrt{2}-1)^{4}(17+12 \sqrt{2})}= \\
= & \sqrt[4]{(17-12 \sqrt{2})(17+12 \sqrt{2})}=\sqrt[4]{17^{2}-2 \cdot 12^{2}}=\sqrt[4]{1}=1
\end{aligned}
$$

Megoldások száma: 15.

