1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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:

    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


    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


    User Avatar
    Homework Helper

    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..
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads for Rationalizing complex root
division of complex number
Help me understand addition of 2 rational fn's