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Math Help - rational number analysis

  1. #1
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    rational number analysis

    Hi there

    I was just wondering if you might be able to help me with this question:

    Show that there is no rational number 's' such that s^2 = 3

    thanks
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  2. #2
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    Quote Originally Posted by daaavo View Post
    Hi there

    I was just wondering if you might be able to help me with this question:

    Show that there is no rational number 's' such that s^2 = 3

    thanks
    Write s=a/b where a,b>1. Then a^2 = 3b^2. Factor a into primes and b into primes. The exponents of the primes of a^2 will all be even similarly with b. However, 3b^2 will make one of the elements (i.e. 3) to be odd. And therefore the two sides do not match up. An impossibility.
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