How to prove that the square root of 2 is irrational

Suppose that the square root of 2 is a rational number, then it must be written in the form of P / Q (P and Q are coprime)
Let P / Q = sqrt (2), then p ^ 2 / Q ^ 2 = 2, that is, P ^ 2 = 2q ^ 2, which is contradictory to the coprime of P and Q, so root 2 is irrational

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