1. The problem statement, all variables and given/known data As the title says. 2. Relevant equations Rational number: a/b for some integers a, b Even number: 2k for some integer k Odd number: 2j+1 for some integer j 3. The attempt at a solution Assume √2 is a rational number. Then it can be expressed a/b for some integers a and b. Reduced to it’s lowest form, a and b cannot both be even numbers. √2 = a/b ----> √2b=a ----> 2b2=a2 ---->a2 is even ----> a is even ----> a=2k for some integer k ----> 2b2=(2k)2 ----> b2=2k2 ----> b is even: a contradiction because both a and b cannot be even. Hence √2 is not a rational number.