I found this standupmaths video on YouTube about the A4 paper puzzle.
I really liked the puzzle and managed to get the answer by using a calculator. However, the answer (which I won't spoil), led me to think that the equation to solve it might simplify - which it does.
In the middle of the simplification, I got this expression:
which for other reasons I suspected to be equal to:
I tried squaring the above and, sure enough, it does give:
My question is, how would I have been able to find the square root of
if I hadn't been able to guess at it? Is there a standard technique? I've tried looking on the web but don't really even know what to search for.