algebra precalculus - Finding the square root of $6-4sqrt{2}$

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:

$$\sqrt{6-4\sqrt{2}}$$

which for other reasons I suspected to be equal to:

$$\ 2-\sqrt{2}$$

I tried squaring the above and, sure enough, it does give:

$$6-4\sqrt{2}$$

My question is, how would I have been able to find the square root of

$$6-4\sqrt{2}$$

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.