How to Simplify a Tricky Fraction?

[math2010]

Homework Statement

How do I simplify the following

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

The Attempt at a Solution

I know that the denominator will be $$1+m^2$$ but I don't know how to simplify the numerator. Can anyone show me how?

 

[Anonymous217]

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.

 

[math2010]

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.

It doesn't seem to change much

$$\frac{(m^2+m)^{\frac{1}{3}} . (1+m^2)^{\frac{1}{2}}}{1+m^2}$$

Should we just add the powers, and what about the terms?

 

[Anonymous217]

What's 1/3 + 1/2?

 

[Mark44]

What's 1/3 + 1/2?

I don't see how that is applicable in this problem. If I'm understanding you correctly, you are trying to convince us that a^1/3b^1/2 can somehow be combined.

 

[Mark44]

It doesn't seem to change much

$$\frac{(m^2+m)^{\frac{1}{3}} . (1+m^2)^{\frac{1}{2}}}{1+m^2}$$

Should we just add the powers, and what about the terms?

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.

 

[Matterwave]

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.