Proof that Square Root of Three is Irrational

Introduction

In The Intuitive Proof of the Infinitude of Primes, I showed you a proof strategy called proof by contradiction.  In this post, we use this strategy to prove that $latex \sqrt{3}$ is irrational.  In proof by contradiction, if the statement P is true, you have to assume the contrary, and then find a contradiction somewhere. Note that the proof in this post is very similar to the proof that $latex \sqrt{2}$ is irrational.

square root of three

Theorem:  $latex \sqrt{3}$ is irrational. Continue reading