# subfield

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• Dec 15th 2008, 07:27 PM
Byun
subfield
Let $K=\mathbb{Q}(\sqrt[n]{a})$, where $a \in \mathbb{Q}, a>0$ and suppose $[K:\mathbb{Q}]=n$.

Let $E$ be any subfield of $K$ and let $[E:\mathbb{Q}]=d$.

Prove that $E=\mathbb{Q}(\sqrt[d]{a})$.