I understand that for a number to be constructible it must be a membeer of the field of constructible numbers $C$ such that $ 0,1 \in C $ and which is closed under addition, subtraction, division, multiplication and square roots.
So is it sufficient to say that $\sqrt[17]{11}$ is not constructible since there is no way to generate the 17th root using ruler and compass construction since 17 is a prime number (and so can definitely not be obtained through repeated square roots)?