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Math Help - Rationalising the denominator.

  1. #1
    Junior Member
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    Rationalising the denominator.

    Just a little hint for this one please.

    \frac {1}{1+ \sqrt{2}+ \sqrt{3}}

    Thank you.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Ting View Post
    Just a little hint for this one please.

    \frac {1}{1+ \sqrt{2}+ \sqrt{3}}

    Thank you.
    First, multiply both numerator and denominator by
    (1 +sqrt(2)) -sqrt(3)
    to rationalize the sqrt(3)

    Or, by (1 +sqrt(3)) -sqrt(2)
    to rationalize the sqrt(2)
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  3. #3
    Junior Member
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    Mar 2008
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    Thank you very much. I should have thought of trying that myself.

    Got

    \frac {1+\sqrt{2}-\sqrt{3}}{2 \sqrt{2}}

    and then:

    \frac {\sqrt{2}}{4}-\frac {\sqrt{6}}{4}+\frac {1}{2}

    Thanks again.
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