# Determine splitting field $K$ over $\mathbb{Q}$ of the polynomial $x^3 - 2$

Determine the splitting field $K$ over $\mathbb{Q}$ of the polynomial $x^3 - 2$

Also determine the basis over $\mathbb{Q}$ and its degree. Can I do this using only first principles?

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Do you know what the roots of $x^3-2$ are? –  Zev Chonoles May 23 '13 at 21:32

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