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Math Help - Surds problem, please explain how?

  1. #1
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    Surds problem, please explain how?

    Hi, could anyone please explain to me how to do this?

    Simplify as far as possible.

    2√2 ......3-2√2
    ----- - ---------
    √6 ...... √2

    Thanks in advance for all your help.
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  2. #2
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    Hello, joz31!

    Simplify as far as possible: . <br />
\frac{2\sqrt{2}}{\sqrt{6}} - \frac{3-2\sqrt{2}}{\sqrt{2}}
    Reduce the first fraction: . \frac{2}{\sqrt{3}} - \frac{3-2\sqrt{2}}{\sqrt{2}}

    Rationalize: . {\color{blue}\frac{\sqrt{3}}{\sqrt{3}}}\cdot\frac{  2}{\sqrt{3}} \:- \:{\color{blue}\frac{\sqrt{2}}{\sqrt{2}}}\cdot\fra  c{3-2\sqrt{2}}{\sqrt{2}} \;\;=\;\;\frac{2\sqrt{3}}{3} \,- \,\frac{3\sqrt{2}-4}{2}

    Get common denominator: . {\color{blue}\frac{2}{2}}\cdot\frac{2\sqrt{3}}{3} \:- \:{\color{blue}\frac{3}{3}}\cdot\frac{3\sqrt{2} - 4}{2}  \;\;=\;\;\frac{4\sqrt{3}}{6} - \frac{9\sqrt{2} - 12}{6}

    Therefore: . \frac{4\sqrt{3} - 9\sqrt{2} + 12}{6}

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  3. #3
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    Thanks heaps for the quick reply!
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