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Math Help - Another Proof

  1. #1
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    Exclamation Another Proof

    Show that the square root of three is not rational.

    I've tried by assuming that it is rational and showing a contradiction...but I hit a wall...any suggestions?
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    Senior Member vincisonfire's Avatar
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    Suppose sqrt(3) is rational. Then it has a unique factorization of prime numbers.
    sqrt(3)=p1*p2*...*pn
    sqrt(3)^2=3^1=p1^2*p2^2*...*pn^2
    On left hand side exponent is odd and all exponents are even on right hand side.
    By uniqueness of factorization of prime we have a contradiction. Thus sqrt(3) is not rational.
    Last edited by vincisonfire; October 15th 2008 at 05:09 PM.
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  3. #3
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    Quote Originally Posted by dolphinlover View Post
    Show that the square root of three is not rational.

    I've tried by assuming that it is rational and showing a contradiction...but I hit a wall...any suggestions?
    You're on the right track.

    Assume that \sqrt{3} = \frac{a}{b} where a and be are integers and their ratio is irreducible.

    You should find that both a and b have a factor of 3, and so their ratio is reducible.
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