If $\alpha ^{2}$ is algebraic over $F$, then show that $\alpha$ is algebraic over $F$.

Question

If $\alpha ^{2}$ is algebraic over $F$, then show that $\alpha$ is algebraic over $F$.

I have only found solutions where it shows the converse. I am not really sure where to start... do I prove the contrapositive and assume that $\alpha$ is not algebraic? I haven't learned much about the degrees of extensions yet.

Answer 1

If $\alpha^2$ is a root of $p(t)\in F[t]$, $\alpha$ is a root of $p(t^2)$, which has degree $2\deg p$.