- #1

- 986

- 9

## Homework Statement

As the title says.

## Homework 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

## 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 ----> 2b

^{2}=a

^{2}---->a

^{2}is even ----> a is even ----> a=2k for some integer k ----> 2b

^{2}=(2k)

^{2}----> b

^{2}=2k

^{2}----> b is even: a contradiction because both a and b cannot be even.

Hence √2 is not a rational number.