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Proving the Square Root of 2 is Irrational

Date: 02/04/2004 at 20:47:40
From: pat
Subject: proving irrationality by using the rational zeroes test

How can you prove that the square root of 2 is irrational 
using the rational zeros test?

Date: 02/04/2004 at 22:43:35
From: Doctor Rob
Subject: Re: proving irrationality by using the rational zeroes test

Thanks for writing to Ask Dr. Math, Pat!

Look at the equation x^2 - 2 = 0.  By the Rational Root Theorem, if
it has a rational root a/b with b > 0, then a must be a divisor of
2 and b must be a divisor of 1 (and so b = 1).  Then show that none
of them is a root, but sqrt(2) is a root.

Can you finish it up?

Feel free to write again if I can help further.

- Doctor Rob, The Math Forum 
Associated Topics:
High School Number Theory

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