Can the square root of any positive integer that is not a perfect square be irrational?

It's not. (1+sqrt(5))/2 is "the golden ratio" (once in a while called "the golden mean"). As for why (1+sqrt(5))/2 is called the golden ratio, the short answer is that it looks nice when things are in that ratio.

The long answer is a trek through ancient philosophy that doesn't interest me all that much.

I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.