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  1. #1
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    Rationalize-help

    1.) (2+√3)/(5+√7)



    2.) (2x+√5x)/(5+√x)



    3.) (2+√15)/(3+4√30m)
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  2. #2
    o_O
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    Take the conjugate of the denominator. For the #1, the conjugate of 5 + \sqrt{7} is: 5 {\color{red}-} \sqrt{7}.

    Take the conjugate and multiply it to both the numerator and denominator:
    \frac{2 + \sqrt{3}}{5 + \sqrt{7}} \cdot \frac{5 {\color{red}-} \sqrt{7}}{5 {\color{red}-} \sqrt{7}} \: \: = \: \: \frac{10 -2\sqrt{7} +5\sqrt{3} - \sqrt{21}}{25 - 7} \: \: = \: \: \ldots

    The other questions use exactly the same method. Post if you have any more problems!
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  3. #3
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    Quote Originally Posted by o_O View Post
    Take the conjugate of the denominator. For the #1, the conjugate of 5 + \sqrt{7} is: 5 {\color{red}-} \sqrt{7}.

    Take the conjugate and multiply it to both the numerator and denominator:
    \frac{2 + \sqrt{3}}{5 + \sqrt{7}} \cdot \frac{5 {\color{red}-} \sqrt{7}}{5 {\color{red}-} \sqrt{7}} \: \: = \: \: \frac{10 -2\sqrt{7} +5\sqrt{3} - \sqrt{21}}{25 - 7} \: \: = \: \: \ldots

    The other questions use exactly the same method. Post if you have any more problems!
    So is that the final answer or would you have to simplyfy it?
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  4. #4
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    Quote Originally Posted by ep78 View Post
    So is that the final answer or would you have to simplyfy it?

    sorry..nevermind..but would you have to split the √21? or just leave the numerator as it is?
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  5. #5
    o_O
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    Yes you would further simplify it. Not much to do though.
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