Square root of a Mersenne number is irrational

Defining a Mersenne Number like this:

k = $2^n -1$

I have to prove that the square root of a Mersenne number is irrational (has no solution in $\mathbb Q$). I know that it can be proven that the square root of a non-perfect square number is always irrational, but is there a particular proof for a Mersenne Number?