Decide whether a field extension contains a given element

Let \omega = \frac{-1}{2} + \frac{\sqrt{3}}{2}i. Decide whether or not \sqrt{3} \in \mathbb{Q}(i,\omega).


Evidently, i(\omega^2 - \omega) = \sqrt{3}; so \sqrt{3} \in \mathbb{Q}(i,\omega).

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