Proving the Square Root of 3 is Irrational

Date: 12/7/95 at 14:13:2
From: Anonymous
Subject: proof in set theory

I have to prove that the square root of 3 is irrational...

First we must assume that

     sqrt(3) = p/q
                                  
I then have

     3 = p^2/q^2
                                
I don't know where to go from there. Please help!

Date: 5/23/96 at 10:39:33
From: Doctor Ethan
Subject: Re: proof in set theory

Hi,

Assume that

         3 = p^2/q^2

where p and q are integers and p/q is in lowest terms. So

     3 q^2 = p^2

So p^2 is divisible by 3. That means that p must be as well, so p^2 is 
divisible by nine.

So

       q^2 = p^2/3

and q^2 is divisible by three.

But that means that p and q are both divisible by three, so they weren't 
in lowest terms, which is a contradiction.

Hope that makes sense. 

-Doctor Ethan
 The Math Forum