Answer:
The proof that √2 is indeed irrational is usually found in college level math texts, but it isn't that difficult to follow. It does not rely on computers at all, but instead is a "proof by contradiction": if √2 WERE a rational number, we'd get a contradiction.
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A proof that the square root of 2 is irrational.
2 = (2k)2/b2
b2 = 2k2