How do I find a splitting field for the polynomial $x^3 - 10$ over $\mathbb Q[\sqrt2]$ ?
I know that elements of $\mathbb Q[\sqrt2]$ are of the form $a + \sqrt2 b$ where $a$ and $b$ are in $\mathbb Q$.
I am taking a course in field theory for the first time so have very less idea on how to proceed.