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Math Help - Proof

  1. #1
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    Proof

    Use:
    There is no rational number whose square equals 2
    to show that there is no rational number whose square equals 2/9.
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    Hello,
    Quote Originally Posted by wvlilgurl View Post
    Use:
    There is no rational number whose square equals 2
    to show that there is no rational number whose square equals 2/9.
    Assume there exists a rational number r whose square equals 2/9 :
    r^2=\frac 29
    hence 9r^2=2

    so (3r)^2=2

    since r is a rational, 3r is a rational.

    But since there is no rational whose square equals 2, we've got a contradiction.
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