rooting irrationally

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For the real math geeks, this month's issue takes you through the calculations your calculator does when calculating the square root of 2. Cool.

On my first day of graduate school, my instructor proved that the square root of 2 is irrational. On his first exam, he asked us to prove that the square root of 12 was irrational. Out of some 40 math students in the room, I was one of only two or three (I think) that got it right. Can you prove that the square root of 12 is irrational?