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Thread: simplifying surd

  1. #1
    Junior Member
    Joined
    Feb 2006
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    simplifying surd

    Think I'm missing something really fundamental here why does

    $\displaystyle
    \frac{16+\sqrt 32}{2}
    $

    Simplify to


    $\displaystyle
    8+\sqrt 8
    $

    and not

    $\displaystyle
    8+\sqrt 16
    $

    and what rules or hints can you give to help simplify surd's in general
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  2. #2
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    Quote Originally Posted by macca101
    Think I'm missing something really fundamental here why does

    $\displaystyle
    \frac{16+\sqrt 32}{2}
    $

    Simplify to


    $\displaystyle
    8+\sqrt 8
    $

    and not

    $\displaystyle
    8+\sqrt 16
    $

    and what rules or hints can you give to help simplify surd's in general
    Because $\displaystyle \frac{\sqrt{32}}{2}\not =\sqrt{16}$, rather,
    $\displaystyle \frac{\sqrt{32}}{2}=\frac{\sqrt{4\cdot 8}}{2}=\frac{2\sqrt{8}}{2}=\sqrt{8}$
    Thus,
    $\displaystyle \frac{16+\sqrt{32}}{2}=8+\sqrt{8}$
    You can still simplify it further.
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