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Math Help - [SOLVED] Basic math taken to a next level...

  1. #1
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    [SOLVED] Basic math taken to a next level...

    Hello everyone!

    During my revision for my June exams (first year engineering) I came across this problem:

     <br /> <br />
\frac{2\sqrt{2} + 2 \sqrt{6}}{\sqrt{2+\sqrt{3}}}<br /> <br />

    Simple math as it seems it kept me busy for 5 hours and stil no results. I know the answer is 4, but the catch is we are not allowed to use calculator. So I'm not interested in an answer, I'm interested in a method.

    Any suggestions please?

    I've already found multiple ways of simplifying it, so that there is no division by a square root but the method is still eluding me...
    Last edited by FifthRider; June 18th 2009 at 01:17 AM. Reason: Oops, typo
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  2. #2
    Senior Member Stroodle's Avatar
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    Is that \frac{2\sqrt 2 +2\sqrt 6}{\sqrt2 +\sqrt3} ?
    Cause that doesn't equal \frac{4}{3}
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  3. #3
    Super Member flyingsquirrel's Avatar
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    Hi,
    Quote Originally Posted by FifthRider View Post
    During my revision for my June exams (first year engineering) I came across this problem:

     <br />
[2*sqrt(2) + 2*sqrt(6)]/[sqrt(2 + sqrt(3))]<br />

    Simple math as it seems it kept me busy for 5 hours and stil no results. I know the answer is 4/3 , but the catch is we are not allowed to use calculator. So I'm not interested in an answer, I'm interested in a method.
    Let A=\frac{2\sqrt{2}+2\sqrt{6}}{\sqrt{2+\sqrt{3}}}. We have A=2\sqrt{2}\cdot \frac{1+\sqrt{3}}{\sqrt{2+\sqrt{3}}} hence A^2=8\cdot \frac{1+2\sqrt{3}+3}{2+\sqrt{3}}=8\times 2 =16 which gives us A=+\sqrt{A^2}=4.
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  4. #4
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    Thanks, feel like kicking myself in the butt. Did I mention that the 5 hours I spent on it was this morning from 12-5? Might explain the elusive answer...

    Thanks again!
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