Can we ask difficult math questions here? More specifically, I mean a math question that involves square roots.
Yes, as long as they really are "puzzles".
We have a lot of mathematics puzzles on this site - nearly 2000 questions in the tag - and many of them are Olympiad-style questions, some even taken from actual Olympiads. Square roots certainly aren't considered "difficult maths" by this site's standards - we've even had a puzzle whose solution required using the Green-Tao theorem!
A few important caveats though, before you post your puzzle:
- Maths puzzles are on-topic; maths problems are not. See Are math-textbook-style problems on topic? for our explanation of the difference between the two. Basically, your puzzle needs to be somehow "interesting" and not formulaic.
- Puzzles involving very advanced maths may be frowned upon. For more details on this rather nebulous policy, see What tricky mathematical questions are on topic here? and Proposed policy on mathematical questions. Basically, the puzzle (not necessarily the solution) should be at least comprehensible to a reasonable subset of Puzzling users. Again, square roots are definitely way below that bar, and I suspect all Olympiad questions easily pass this criterion. Just don't post something which requires a deep understanding of the proof of Fermat's Last Theorem ;-)
- You must cite your source. If you're taking a puzzle from an actual olympiad, or a similar competition, or a puzzle book, remember to state in the body of your question where you found it. Without this acknowledgement, your question runs the risk of being deleted for 'plagiarism'.
There's certainly no objection to square roots, and plenty of questions have been asked here that involve some quite tricky mathematics. However, PSE tends to frown on questions that are mathematics problems as opposed to mathematical puzzles. Roughly, the question to be asking is: is this more something you might solve for fun or the sort of exercise you'd find in a textbook or mathematics class homework?
Take a look at the "mathematics" tag to get an idea of the sort of mathematical question that gets asked here (and which ones have received lots of upvotes or good answers).