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Rationalizing complex root

  1. Nov 9, 2015 #1
    1. The problem statement, all variables and given/known data

    If ##\sqrt{\frac{10+4\sqrt{6}}{10-4\sqrt{6}}}=a+b\sqrt{6}##, then a+b is ?

    A) 8
    B) 7
    C) 6
    D) 5
    E) 4

    3. The attempt at a solution

    This is my attempt:
    ##\sqrt{\frac{10+4\sqrt{6}}{10-4\sqrt{6}}}=\sqrt{\frac{10+4\sqrt{6}*(10+4\sqrt{6})}{10-4\sqrt{6}*(10+4\sqrt{6})}}=\sqrt{\frac{196+80\sqrt{6}}{4}}=\sqrt{49+20\sqrt{6}}##

    Then, I got stuck.. I have no idea how to convert to form a+b√6
    Please help..
     
  2. jcsd
  3. Nov 9, 2015 #2

    Mark44

    Staff: Mentor

    Square both sides of your original equation and then rationalize the denominator on the left side.
    You should get something like m + n√(6) on one side and r + s√(6) on the other side. You can equate m with r and n with s to get two equations involving a and b.
     
  4. Nov 9, 2015 #3

    ehild

    User Avatar
    Homework Helper
    Gold Member

    You have to use parentheses. The correct form is ##\sqrt{\frac{10+4\sqrt{6}}{10-4\sqrt{6}}}=\sqrt{\frac{(10+4\sqrt{6})*(10+4\sqrt{6})}{(10-4\sqrt{6})*(10+4\sqrt{6})}}##
    Is not the numerator the square of something? What is its square root?
     
  5. Nov 9, 2015 #4

    Thanks.. a is 5 and b is 2 , so a+b is 7..
     
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