Proof: If n is a perfect square, $\,n+2\,$ is NOT a perfect square "Prove that if n is a perfect square, $\,n+2\,$ is NOT a perfect square." I'm having trouble picking a method to prove this. Would contraposition be a good option (or even work for that matter)? If not, how about contradiction?

I don't know that you should pick a proof strategy before you have played with the hypotheses a little bit.  In my experience, thinking about the hypotheses tends to suggest natural proof strategies.
In this case, I would think like this: perfect squares are the partial sums of the series of positive odd numbers, so you can't get to the next perfect square by adding $2$.  This suggests contradiction.
Alternatively -- and this would suggest proof by contraposition -- if you have arranged $n$ tiles in a square, and you remove two, can you rearrange those into a smaller square?
