As the title says.
Rational number: a/b for some integers a, b
Even number: 2k for some integer k
Odd number: 2j+1 for some integer j
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.