Question: Prove that $\displaystyle\sum_{i=1}^n \sqrt{i}$ is irrational for all $n \geq 2$.
My attempts: My first instict was going straight to proving this with mathematical induction, however I'm unsure how this would work as if $n$ if a square number it may be a little problematic with the $n=k+1$ case. Perhaps there is another way of doing it that doesn't require mathematical induction. Any help or guidance would be greatly appreciated!
