uclb5550

N must be integer, otherwise, the answer will be E.

30=2*3*5  30 is factor of N^2, which means N must be 30 at least.
2*3*5*M=N^2  in order to set up the equation, M must be 2*3*5 at least. therefore, the conclusion is out here. 30 must a factor of N.

clear?

uclb5550

answer is A. sorry, my words makes some perplexity for you. what i mean is, if as your speculation puts it--N is irrational number, the answer would be E.

by the way, the reason why B is wrong is the N can be 15.