radicals - Prove or disprove that $sqrt{2+frac{1}{n}}$ is irrational for $n in mathbb{Z}^+$

I have good reason to suspect that $\sqrt{2+\frac{1}{n}}$ is irrational for all $n \in \mathbb{Z}^+$ but a proof of this eludes me. I've tried proof by contradiction have had no success. I've also tried induction where clearly the base case is true, i.e. $\sqrt{2+1}=\sqrt{3}$ is irrational, but I haven't been able to show the induction step.