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I find this fact rather spectacular, but my question is why is this true? I have seen the formal proof for the irrationality of root 2 so I could vaguely see how one could prove that all (apart from sq numbers) integer square roots are irrational, but the real question I'm asking here is WHY is it true - is there a deeper mathematical reason? Or is it simply down to a coincidence?

Thank you for your help in advance.