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Math Help - Surds Help

  1. #1
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    Surds Help

    Hey I'm having problems figuring out how to do this surd.

    16/(√20+√12)

    I know the answer is 4(√5-√3) but can you plz give me a step by step answer on how to do this...thanks.
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  2. #2
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    Quote Originally Posted by digideens
    Hey I'm having problems figuring out how to do this surd.

    16/(√20+√12)

    I know the answer is 4(√5-√3) but can you plz give me a step by step answer on how to do this...thanks.
    Multiply both top and bottom by \sqrt{20}-\sqrt{12}:

    <br />
\frac{16}{\sqrt{20}+\sqrt{12}}=\frac{16(\sqrt{20}-\sqrt{12})}{(\sqrt{20}+\sqrt{12})(\sqrt{20}-\sqrt{12})}<br />


    <br />
=\frac{16(\sqrt{20}-\sqrt{12})}{20-12}=4(\sqrt{5}-\sqrt{3})<br />

    RonL
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  3. #3
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    is there another step between the

    =16(√20-√12)/20-12 and
    = 4(√5-√3)
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  4. #4
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    Quote Originally Posted by digideens
    is there another step between the

    =16(√20-√12)/20-12 and
    = 4(√5-√3)
    Yes,
    You have,
    \frac{16(\sqrt{20}-\sqrt{12})}{8}
    Simplyfy fraction to 2(\sqrt{20}-\sqrt{12})
    Now,
    \sqrt{12}=\sqrt{4\cdot 3}=2\sqrt{3}
    \sqrt{20}=\sqrt{4\cdot 5}=2\sqrt{5}
    Thus,
    2(2\sqrt{5}-2\sqrt{3})
    Factor the two,
    4(\sqrt{5}-\sqrt{3})
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  5. #5
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    Oh right, I get it now..thanks a lot.
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