\(\sqrt{2}\) \(^{5}\) can also be written as \(\sqrt{2}\) x \(\sqrt{2}\) x \(\sqrt{2}\) x \(\sqrt{2}\) x \(\sqrt{2}\) .
\(\sqrt{2}\) x \(\sqrt{2}\) = 2
2 x \(\sqrt{2}\) = 2\(\sqrt{2}\)
2\(\sqrt{2}\) x \(\sqrt{2}\) = (2)(2) = 4
4 x \(\sqrt{2}\) = 4\(\sqrt{2}\)
The final answer is 4 \(\sqrt{2}\), which is equal to 5.656854249.