My question is for $\mathbb{Q} \lt K \lt \mathbb{R}$ show that $|K:\mathbb{Q}|$ is a power of 2.
I know you have to use the definitions of radical and galois extensions but I don't understand how you are going to manipulate them to obtain a basis of $\mathbb{Q}$ with $2^n$ elements over $K$.
A similar question is asked here however it asks for a proof with respect to another proof whereas I will accept any method.
Radical and Galois Field Extension has degree $2^n$