I am revising for my algebraic number theory exam and was hoping I could get on some help on the following two questions:
a) Let $\alpha$ be algebraic over a field $K$ of odd degree. Show that $K(\alpha) = K(\alpha^2)$
b) Let $L = K(\alpha, \beta)$, with deg$_K(\alpha) = m, \, $ deg$_K(\beta) = n, \,$ and gcd$(m,n) = 1$. Show that $[L : K] = mn.$
I really don't know where to start with either of these problems.