Proving sqrt(5) is irrational using the prime lemma

[mathwonk]

here's another explanation of gibz's proof which is actually also my favorite: if sqrt(n) = a/b is in lowest form, then n = a^2/b^2 is also in lowest form, but lowest form is unique and n/1 is a lowest form for n, so b^2 = 1 and a^2 = n. i.e. if sqrt(n) is rational, then sqrt(n) is an integer.