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Math Help - Simplifying Surd

  1. #1
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    Simplifying Surd

    Hi,

    Could someone please show the steps that go to simplifying the below:

    [SQRT(6) + 3*SQRT(2)] / [3+SQRT(5)]

    Thanks, your help will be greatly appreciated.

    Andy
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  2. #2
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    Re: Simplifying Surd

    Quote Originally Posted by andy000 View Post
    Hi,

    Could someone please show the steps that go to simplifying the below:

    [SQRT(6) + 3*SQRT(2)] / [3+SQRT(5)]

    Thanks, your help will be greatly appreciated.

    Andy
    $\dfrac{\sqrt{6}+3\sqrt{2}}{3+\sqrt{5}}=\dfrac{ \sqrt{6}+3\sqrt{2}}{3+\sqrt{5}}\cdot 1=$

    $\dfrac{\sqrt{6}+3\sqrt{2}}{3+\sqrt{5}}\cdot \dfrac{3-\sqrt{5}}{3-\sqrt{5}}=$

    $\dfrac{3\sqrt{6}+9\sqrt{2}-\sqrt{30}-3\sqrt{10}}{9-5}=$

    $\dfrac{3\sqrt{6}+9\sqrt{2}-\sqrt{30}-3\sqrt{10}}{4}$

    this form should be acceptable. You can tinker with it further to get

    $\dfrac{3\sqrt{2}\sqrt{3}+9\sqrt{2}-\sqrt{2}\sqrt{3}\sqrt{5}-3\sqrt{2}\sqrt{5}}{4}=$

    $\dfrac{\sqrt{2} \left(3\sqrt{3}+9-\sqrt{3} \sqrt{5}-3\sqrt{5}\right)}{4}=$

    $\dfrac{\sqrt{2}\left(3+\sqrt{3}\right)\left(3-\sqrt{5}\right)}{4}$
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  3. #3
    Junior Member
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    Re: Simplifying Surd

    Thanks very much for the quick reply. I did get the answer out to that first solution, but when I tried to simplify further I made a huge mess of it and figured I had been going about it the wrong way.
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