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Math Help - Perfect Squares

  1. #1
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    Post Perfect Squares

    why isnt 2(with a 3 above it) x 3(with a 6 above it) x 13(with a 2 above it) not a perfect square number?


    also,can anyone explain a square number?
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  2. #2
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    re: Perfect Squares

    Quote Originally Posted by corihawke View Post
    why isnt 2(with a 3 above it) x 3(with a 6 above it) x 13(with a 2 above it) not a perfect square number?


    also,can anyone explain a square number?
    A perfect square can be written as \displaystyle a^2, where \displaystyle a is an integer.

    \displaystyle 3^6 = \left(3^3\right)^2 and \displaystyle 13^2 are perfect squares, but \displaystyle 2^3 = \left(2^{\frac{3}{2}}\right)^2 is not.
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  3. #3
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    re: Perfect Squares

    a perfect square is an integer times itself

    3*3=9=3^2
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  4. #4
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    Re: Perfect Squares

    remember that anything raised to a power can be written as the number raised to a factor of that power, and then raised to the other factor:

    3^6 = (3^3)^2

    So anything raised to an EVEN power is a perfect square.

    If you have several factors, each raised to an even power, they can all be rewritten as a perfect square. Remember:

    (a^2)(b^2) = (a*b)^2

    So if all 3 of your factors can be written like this, the whole thing can be written as a perfect square. But one of the numbers you gave was raised to an ODD power, meaning it can't be rewritten as a perfect square.

    Aaron McDevitt
    Last edited by mr fantastic; September 6th 2011 at 03:50 PM. Reason: Deleted advertising link.
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