Square root of 2 is not the ratio of integers. It is irrational.
Rational numbers are the RATIO of integers. That is why they are called rational numbers. Irrational numbers are not the ratio of integers. That is why they are called irrational numbers. Since sqrt(2) was proven to be not rational, it was proven to not be the ratio of integers. (a+b)^2 + (a-b)^2 =... Sign in to see full entry.