Proving the Square Root of 2 is IrrationalDate: 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 http://mathforum.org/dr.math/ |
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