First, you assume root 2 is rational, so write it as p/q in lowest terms. Squaring gives p² = 2q², meaning p² is even, so p is even. Write p=2k, substitute, and you find q² is also even, so q is even. But if both are even, p/q wasn't in lowest terms—contradiction. Bas, it's irrational. Teaching this to my tenth-standard tutees in Andheri, I see their eyes light up at the 'lowest terms' trick—it's the same joy I get when my daughter quizzes me, yaar.
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