Let $\displaystyle F $ be a subfield of $\displaystyle \mathbb{R} $. Let $\displaystyle a $ be an element of $\displaystyle F $ and let $\displaystyle K=F(\sqrt[n]{a}) $ where $\displaystyle \sqrt[n]{a} $ denotes the real $\displaystyle n^{th} $ root of $\displaystyle a $.

Prove thatif $\displaystyle L $ is any Galois extension of $\displaystyle F $ contained in $\displaystyle K $ then $\displaystyle [L:F]\leq2 $.

I have no idea how to approach this problem.

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