Determine the minimal polynomial of $\sqrt 3+\sqrt 5$ I am struggling in finding the minimal polynomial of $\sqrt{3}+\sqrt{5}\in \mathbb C$ over $\mathbb Q$
Any ideas? I tried to consider its square but it did not helped..

You should be able to find a  monic quartic $p(x)\in\Bbb Q[x]$ having $\sqrt3\pm\sqrt5$ and $-\sqrt3\pm\sqrt5$ as its roots. There are only $3$  monic quadratic and $3$ monic cubic factors of $p(x)$ of which $\sqrt3+\sqrt5$ is a root, so it shouldn't be tricky to check whether any of those factors is in $\Bbb Q[x]$. In fact, you shouldn't even have to check the cubic factors. (Do you see why?)
