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Thread: simplifying surd

  1. April 10th 2006, 11:37 AM #1
    macca101
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    simplifying surd

    Think I'm missing something really fundamental here why does

    <br /> \frac{16+\sqrt 32}{2}<br />

    Simplify to


    <br /> 8+\sqrt 8<br />

    and not

    <br /> 8+\sqrt 16<br />

    and what rules or hints can you give to help simplify surd's in general
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  2. April 10th 2006, 11:41 AM #2
    ThePerfectHacker
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    Quote Originally Posted by macca101
    Think I'm missing something really fundamental here why does

    <br /> \frac{16+\sqrt 32}{2}<br />

    Simplify to


    <br /> 8+\sqrt 8<br />

    and not

    <br /> 8+\sqrt 16<br />

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