In this math lesson we go over a nice and easy proof that the square root of 2 is irrational. We suppose for the sake of contradiction that the square root of 2 is rational and we write it as a fraction in lowest terms. From here, we can prove that if the square root of 2 does in fact equal this fraction, then both the numerator and denominator are even. Thus, it contradicts our original assumption that the fraction is in lowest terms (and thus, they have no common factors and hence cannot both be even), thus our original assumption must be wrong and therefore the opposite must be true. So the square root of 2 is indeed irrational.

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