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Homework Help: Fraction Simplification

  1. Mar 17, 2010 #1
    1. The problem statement, all variables and given/known data

    How do I simplify the following

    [tex]\frac{\sqrt[3]{m^2+m} . \sqrt{1+m^2}}{\sqrt{1+m^2}.\sqrt{1+m^2}}[/tex]

    3. The attempt at a solution

    I know that the denominator will be [tex]1+m^2[/tex] but I don't know how to simplify the numerator. Can anyone show me how?
  2. jcsd
  3. Mar 17, 2010 #2
    Try writing out the powers as a fraction. That is, let the square roots be ^(1/2) and such. It'll be easier to see as you just add the fractions.
  4. Mar 17, 2010 #3
    It doesn't seem to change much

    [tex]\frac{(m^2+m)^{\frac{1}{3}} . (1+m^2)^{\frac{1}{2}}}{1+m^2}[/tex]

    Should we just add the powers, and what about the terms?
    Last edited: Mar 17, 2010
  5. Mar 17, 2010 #4
    What's 1/3 + 1/2?
  6. Mar 17, 2010 #5


    Staff: Mentor

    I don't see how that is applicable in this problem. If I'm understanding you correctly, you are trying to convince us that a1/3b1/2 can somehow be combined.
  7. Mar 17, 2010 #6


    Staff: Mentor

    I think this is about all you can do by way of simplification. The two factors in the numerator have different bases, so can't be combined.
  8. Mar 17, 2010 #7


    User Avatar
    Science Advisor
    Gold Member

    Are you sure the first term is m^2+m not m^3+m? cus then, you could factor out an m and go from there.

    Otherwise, I see no way of simplifying this expression other than canceling out one sqrt(1+m^2) from top and bottom.
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