Why is the intersection of Q($\sqrt[n]{a}$) and Q(nth root of unity) Galois? (a>0, n an integer)

Question

With this, I can show the intersection is either Q or Q($\sqrt{a}$). All I have is that their intersection must be real and all subfields of Q($\sqrt[n]{a}$) are of the form Q($\sqrt[d]{a}$) where d|n.