Proving the Square Root of 3 is IrrationalDate: 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 |
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