- Thread starter
- #1

- Mar 10, 2012

- 834

Only one approach comes to my mind. Let $r_1, r_2 \in \mathbb{Q}$ such that $a+b\sqrt{2}=(r_1+r_2\sqrt{2})^2$. This gives $a=r_1^2+2r_2^2, b=2r_1r_2$. I need to somehow show that $r_1, r_2$ are integers. I played with the above equations putting $r_i=p_i/q_i$ with $\gcd (p_i,q_i)=1$. But I couldn't conclude anything.