I'm following Isaacs' Algebra and I need to prove that the field $K$ of constructible numbers is the smallest subfield of $\mathbb{C}$ such that is closed under taking square root.
I already know that $K$ is in fact a field and that if $\alpha \in \mathbb{C}$ such that $\alpha^2\in K$ then $\alpha\in K$ but I don't know how to prove that is the smallest subfield that verifies that property.