If $a$ is constructible, then $\sqrt a$ is constructible. Furthermore, if $a,b,c$ are constructible, then every root of $ax^2+bx+c$ is constructible.
I think I know how to prove the first sentence but I don't know about the second part. Can someone give a proof of this please.
Quadratic Formula
Roots of the quadratic polynomial $ax^2+bx+c$ are $\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. The field of constructible numbers are closed under addition, multiplication and roots, so, $a,b,c$ constructible implies the roots are constructible.