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Thread: simplifying under a radical

  1. #1
    Junior Member
    Joined
    May 2009
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    66

    simplifying under a radical

    Can

    $\displaystyle \sqrt{9-x^2}$

    be simplified to

    $\displaystyle 3-x$

    ?
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  2. #2
    Senior Member I-Think's Avatar
    Joined
    Apr 2009
    Posts
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    No, because $\displaystyle 9-x^2=(3-x)(3+x)$
    So$\displaystyle \sqrt{9-x^2}=\sqrt{(3-x)(3+x)}$

    You can even put in a number to test.
    Let $\displaystyle x=1$

    For $\displaystyle x=1$
    $\displaystyle \sqrt{9-x^2}=2\sqrt{2}$
    While
    $\displaystyle 3-x=2$
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