Show that the polynomial
$$ x^3 - 3$$ Is irreducible over
$$ Q(i, \sqrt2 ) $$
I'm a little stuck as I don't think I can use Eisenstein's criterion as we're not over the rationals. Also I know that the roots of the polynomial are $ \sqrt 3 $ followed by $\omega \sqrt 3 $ and $\omega^2 \sqrt 3 $ However I don't really know how to use this imformation to prove the polynomial is irreducible.