Question

prove that 2 root 2 is an irrational number

Answer 1

Proof that the square root of 2 is irrational. Assume is rational, i.e. it can be expressed as a rational fraction of the form , where and are two relatively prime integers. Now, since , we have , or . Since is even, must be even, and since is even, so is .
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Answer 2

A proof that the square root of 2 is irrational. ... The proof that √2 is indeed irrational is usually found in college level math texts, but it isn't that difficult to follow. It does not rely on computers at all, but instead is a "proof by contradiction": if √2WERE a rational number, we'd get a contradiction.