Prove that √2 is irrational.

Assume √2 = p/q in lowest terms. Then p² = 2q², so p is even; writing p = 2m gives 4m² = 2q², so q² = 2m² and q is also even. But then p and q share the factor 2, which contradicts the assumption that the fraction was in lowest terms, so √2 cannot be rational.

No citable source has been recorded for this record. Treat it as practice material, not as fact.

Explanation

This is the classical proof by contradiction.