0
$\begingroup$

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

  • 4
    If you can solve $a^2=2b^2$, then $2=\left(\frac{a}{b}\right)^2$ which means that the square root of $2$ is rational. See the linked page for some proofs that this is impossible.2011-11-07

1 Answers 1

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.