(adsbygoogle = window.adsbygoogle || []).push({}); 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 ----> 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.

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# Prove √2 is irrational

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