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Math Help - Radical help with radicals!

  1. #1
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    Radical help with radicals!

    I am trying to help my daughter with this problem

    2+square root of 5 over 3 - square root of 6. Please come to my rescue!
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  2. #2
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    have your daughter multiply numerator and denominator by

    3 + \sqrt{6}

    then simplify.
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  3. #3
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    Not 3-square root of 6?
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  4. #4
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    Quote Originally Posted by mommyneedshelp View Post
    I am trying to help my daughter with this problem

    2+square root of 5 over 3 - square root of 6. Please come to my rescue!
    In a fraction, you do not keep a surd ( \sqrt{x}) on the denominator so when it says to simplify the expression, your aim is to remove the surd from the denominator.

    \frac{2+\sqrt{5}}{3-\sqrt{6}}

    Multiply the numerator and the denominator by the conjugate of the denominator which is 3+\sqrt{6}

    \left(\frac{2+\sqrt{5}}{3-\sqrt{6}}\right)\left(\frac{3+\sqrt{6}}{3+\sqrt{6}  }\right)

    Multiply all the expressions. Numerator with numerator and denominator with denominator.

    =\frac{6 + 2\sqrt{6} + 3\sqrt{5} +\sqrt{30}}{9 + 3\sqrt{6} - 3\sqrt{6} -6}

    =\frac{6 + 2\sqrt{6} + 3\sqrt{5} +\sqrt{30}}{3}
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  5. #5
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    Thank you so much for your help!
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