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by Kitty on September 22nd, 2008

Kitty

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Cassify each of the following as rational or irrational number. 6.76776777677776..., 1/square root 15, square root 32/ squareroot 2

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  • by Quirkie on September 22nd, 2008

    Quirkie

    Rational numbers always repeat when written as a decimal.
    The first number you wrote cannot repeat, as each sequence of 7s is unique. Once you see a run of n 7s surrounded by sixes, that never occurs again.

    1/sqrt(15)
    is irrational using reductio ad adsurbum.
    If it is rational, then sqrt(15) is also rational.
    If sqrt(15) is rational then it is p/q, a fraction with no common factor.
    sqrt(15) = p/q
    15q^2 = p^2
    Therefore p has a factor of 15. It must be 15r for some other integer r.
    So 15q^2 = 225r^2
    q^2 = 15r^2
    so q has a factor of 15 too. Contradiction!

    sqrt(32)/sqrt(2) = sqrt(16) = 4
    That's rational.

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