Can a^2 = 2b^2 have a solution where a, b are in Z but not zero?

Question

Possible Duplicate:
How can you prove that the square root of two is irrational?

Can $a^2 = 2b^2$ have a solution where $a, b$ are in $\mathbb{Z}$ but not zero?

$\mathbb{Z}$ = positive and negative whole numbers

Answer 1

If you take square root of the both sides you get:

$|a|=\sqrt{2} \cdot |b|$

So the LHS represents an integer while RHS represents an irrational number therefore equality isn't true so there is no solution of this equation in the set of integers without zero.