Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 0 down vote favorite

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

share|improve this question
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. – Eric♦ Nov 7 '11 at 11:34

marked as duplicate by Eric♦, Gerry Myerson, Hans Lundmark, JavaMan, lhf Nov 7 '11 at 11:40

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

1 Answer

up vote 1 down vote

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.

share|improve this answer

Not the answer you're looking for? Browse other questions tagged or ask your own question.