field theory - If $k_1, ldots, k_n$ are non-square, pairwise coprime, then $sqrt {k_n} not in mathbf{Q}(sqrt {k_1}, ldots, sqrt {k_{n-1}})$

Seems intuitive. Like the fact that $\sqrt 3 \not \in \mathbf{Q}(\sqrt 2)$. But how to approach actually proving it? The proof of this fact doesn't seem to generalize well.