Definition:Linearly Irrational Number

Definition

A number $n$ is linearly irrational if $n$ irrational but its square $n^2$ is rational.

Thus, the set of the linearly irrational numbers is:

$\set {x \in \R \setminus \Q : x^2 \in \Q}$

Linguistic Note

The term linearly irrational was invented by $\mathsf{Pr} \infty \mathsf{fWiki}$.

As such, it is not generally expected to be seen in this context outside $\mathsf{Pr} \infty \mathsf{fWiki}$.