Definition:Squarely Irrational Number

Definition
A number is squarely irrational if both the number itself and its square is irrational.

Thus, the set of the squarely irrational numbers is $\left\{{x \in \R \setminus \Q : x^2 \in \R \setminus \Q}\right\}$.

Also see

 * Definition:Irrational Line Segment