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Math Help - Rationalize the Denominator

  1. #1
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    Rationalize the Denominator



    I can't seem to solve this one. I tried reversing the signs, which didn't work for me. How do I solve this one?
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  2. #2
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    Re: Rationalize the Denominator

    Quote Originally Posted by Diesal View Post
    Multiply numerator and denominator by (1-\sqrt{3}+\sqrt{5})
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  3. #3
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    Re: Rationalize the Denominator

    that won't quite do the job.

    (1 + \sqrt{3} - \sqrt{5})(1 - \sqrt{3} + \sqrt{5}) = 1^2 - (\sqrt{3} - \sqrt{5})^2

     = 1 - (3 - 2\sqrt{15} + 5) = -7 + 2\sqrt{15}, which certainly isn't rational.

    i propose instead multiplying top and bottom by:

    7 + 3\sqrt{3} + \sqrt{5} + 2\sqrt{15}, since:

    (1 + \sqrt{3} - \sqrt{5})(7 + 3\sqrt{3} + \sqrt{5} + 2\sqrt{15}) = 11
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  4. #4
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    Re: Rationalize the Denominator

    You are correct. I entered is incorrectly into my CAS.
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  5. #5
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    Re: Rationalize the Denominator

    Quote Originally Posted by Deveno View Post
    that won't quite do the job.

    (1 + \sqrt{3} - \sqrt{5})(1 - \sqrt{3} + \sqrt{5}) = 1^2 - (\sqrt{3} - \sqrt{5})^2

     = 1 - (3 - 2\sqrt{15} + 5) = -7 + 2\sqrt{15}, which certainly isn't rational.
    Though you could then multiply top and bottom by \displaystyle \begin{align*} -7 - 2\sqrt{15} \end{align*}...
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