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Math Help - Rationalize the denominator and simplify - help

  1. #1
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    Rationalize the denominator and simplify - help

    √(81/40)
    √81/√40=9/√40

    In order to rationalize the denominator, I begin by factoring the denominator 40.
    40 = 2 x 2 x 2 x 5

    I am not getting anywhere with this line of logic. What am I doing wrong??
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    Quote Originally Posted by mcruz65 View Post
    √(81/40)
    √81/√40=9/√40

    In order to rationalize the denominator, I begin by factoring the denominator 40.
    40 = 2 x 2 x 2 x 5

    I am not getting anywhere with this line of logic. What am I doing wrong??

    \sqrt{40}=\sqrt{4}\sqrt{10}=2\sqrt{10}

    Tonio
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  3. #3
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    Quote Originally Posted by mcruz65 View Post
    √(81/40)
    √81/√40=9/√40

    In order to rationalize the denominator, I begin by factoring the denominator 40.
    40 = 2 x 2 x 2 x 5

    I am not getting anywhere with this line of logic. What am I doing wrong??
    Hi mcruz65,

    You have it down to \frac{9}{\sqrt{40}}

    Let's think of the largest perfect square factor of 40. That would be 4 because 4 times 10 is 40. So, rewrite

    \frac{9}{\sqrt{40}}=\frac{9}{\sqrt{4\cdot10}}=\fra  c{9}{2\sqrt{10}}

    Now, to rationalize the denominator, we must multiply both numerator and denominator by \sqrt{10}.

    \frac{9}{2\sqrt{10}}\cdot \frac{\sqrt{10}}{\sqrt{10}}=\frac{9\sqrt{10}}{20}
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