The $n$-th root of $(1+q^n)^2$ is irrational

Question

Let $0<q<1$ be rational. I am suspecting that $\sqrt[n]{(1+q^n)^2}$ is irrational. Can someone please help me to prove or to disprove this?

• $n=1$ and $n=2$ are simple cases. I am interested in $n>2$.