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Math Help - rationalize denominator

  1. #1
    Senior Member euclid2's Avatar
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    rationalize denominator

    rationalize the denominator \frac{\sqrt3 - \sqrt 2}{\sqrt 3 + \sqrt 2}
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by euclid2 View Post
    rationalize the denominator \frac{\sqrt3 - \sqrt 2}{\sqrt 3 + \sqrt 2}
    Multiply the numerator and denominator by  \sqrt3 - \sqrt 2
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  3. #3
    Senior Member euclid2's Avatar
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    Quote Originally Posted by harish21 View Post
    Multiply the numerator and denominator by  \sqrt3 - \sqrt 2
    i know to multiply by the conjugate, i just can't get the right answer
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  4. #4
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by euclid2 View Post
    i know to multiply by the conjugate, i just can't get the right answer
    \frac{\sqrt3 - \sqrt 2}{\sqrt 3 + \sqrt 2}

    = \frac{\sqrt3 - \sqrt 2}{\sqrt 3 + \sqrt 2} \times \frac{\sqrt3 - \sqrt 2}{\sqrt 3 - \sqrt 2}

    = \frac{(\sqrt3 - \sqrt2)^2}{(\sqrt3)^2 -(\sqrt2)^2}

    = \frac{(\sqrt3 - \sqrt2)^2}{3-2}

    Can you finish it now?
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  5. #5
    Senior Member euclid2's Avatar
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    Quote Originally Posted by harish21 View Post
    \frac{\sqrt3 - \sqrt 2}{\sqrt 3 + \sqrt 2}

    = \frac{\sqrt3 - \sqrt 2}{\sqrt 3 + \sqrt 2} \times \frac{\sqrt3 - \sqrt 2}{\sqrt 3 - \sqrt 2}

    = \frac{(\sqrt3 - \sqrt2)^2}{(\sqrt3)^2 -(\sqrt2)^2}

    = \frac{(\sqrt3 - \sqrt2)^2}{3-2}

    Can you finish it now?
    i keep getting 5/1 but the answer says 5-2root6
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  6. #6
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by euclid2 View Post
    i keep getting 5/1 but the answer says 5-2root6
    Remember:  (a-b)^2 = a^2 -2ab + b^2<br />


    \therefore (\sqrt3 - \sqrt2)^2 = (\sqrt3)^2 - 2 \sqrt3 \sqrt2 +(\sqrt2)^2

    = 3 - 2 \sqrt6 +2
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