# A Proof that the Square Root of 2 is Irational

Submitted by Isoscel on Tue, 09/25/2007 - 23:10.

We shall proof that the square root of 2 is irational.

Let's presume the contrary:

is rational.

Then:

with m, n integer numbers and m and n relatively prime ( is an irreducible fraction).

so:

So is even. This means that m is even. So there is an k with .

So is even. This means that n is even too.

Contradiction because m and n are relatively prime.