# Simplifying the radicals

Algebra Level 3

The value of $$S$$ is an integer $$I$$. Enter the value of $$I$$.

$S=\sqrt[5] {41+29\sqrt {2}}-\sqrt[5] {29\sqrt {2}-41}$

You may not use a calculator.

$$\textbf{Assumptions}$$

Consider $$\sqrt[5] {a}$$ to be the principal fifth root of $$a \ \forall a \in \mathbb{R}$$.

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