Galois Theory: Are separable and normal equivalent?

Question

I have to proof the following Theorem

Theorem: Let $\mathbb{Q} \subseteq L$ be a normal field extension with $L \subseteq R$ and $[L:\mathbb{Q}]=2^\lambda$. Then every $\alpha \in L$ is constructible.

Hint: use the fact that $L$ is also separable and therefore $[L:\mathbb{Q}]$ is a Galois extension.

But why is $L$ also separable?

Thanks a lot in advance!

Answer 1

In characteristic 0, every extension is separable.