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Math Help - Quotient and powers problem

  1. #1
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    Unhappy Quotient and powers problem

    Hello all,

    I'm having one of those moments staring at some working in my textbook that I just can't get my head around. I'd rather have a poke in the right direction than a straight solution, but whatever is easier for you guys!

    There are two steps in this working, I just cant see how to get from one to the next. I've tried writing it out in as many ways as I can think of, but I know I'm just missing that one tiny connection!

    From this \frac{1}{200}\frac{x^2+y^2}{\sqrt{x^2+y^2}} to this \frac{1}{200}\sqrt{x^2+y^2}

    In fact, ignore the 1/200. It's just the second quotient I'm struggling with...
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  2. #2
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    If we say that x^2 + y^2 = a

    Then we have a/sqrt(a)

    anything divided by the square root of itself = the square root of itself,

    so a/sqrt(a) = sqrt(a) = sqrt(x^2 + y^2)
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  3. #3
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    Quote Originally Posted by sirellwood View Post
    If we say that x^2 + y^2 = a

    Then we have a/sqrt(a)

    anything divided by the square root of itself = the square root of itself,

    so a/sqrt(a) = sqrt(a) = sqrt(x^2 + y^2)
    And why does this work? Because, if a is positive,

    \frac{a}{\sqrt{a}}=\frac{\sqrt{a}\sqrt{a}}{\sqrt{a  }}=\sqrt{a},

    by virtue of cancellation.
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  4. #4
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    Multiply both numerator and denominator by \sqrt{x^2 + y^2}
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  5. #5
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    Quote Originally Posted by VincentP View Post
    Multiply both numerator and denominator by \sqrt{x^2 + y^2}
    That works, too.
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