Proving √2 is Irrational: A Brief Explanation

[Jamin2112]

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 ----> 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.

 

[Petek]

Your proof is correct!