Rationalizing Denominators: Understanding the Process

[majormuss]

Homework Statement

I am confused with this equation I found online... It seems wrong to me, I need help.
My question is,why did the person who worked taht equation use a x^2 to rationalize the equation when the actual equation was an x^3??
http://tutorial.math.lamar.edu/Classes/Alg/Radicals_files/eq0081MP.gif

Homework Equations

The Attempt at a Solution

 

[Dick]

Because the fifth root of x^2*x^3=x^5 is x. How would you do it??

 

[majormuss]

Because the fifth root of x^2*x^3=x^5 is x. How would you do it??

no my question is... why was x^2 used instead of x^3 to rationalize the denominator? my thinking is if x^2 is the denominator then why use x^3 to rationalize it?

 

[HallsofIvy]

Because $x^2*x^3= x^5$ as Dick said. The crucial point is that it is the fifth root that is to be rationalized. You have to multiply what ever power is necessary to get a fifth power inside the fifth root.

In general to rationalize the denominator of $1/\sqrt[n]{x^m}$ you need to multiply numerator and denominator by $\sqrt[n]{x^{n-m}}$. That way, in the denominator you will have $\sqrt[n]{x^nx^{n-m}}= \sqrt[n]{x^n}= x$.

 

[majormuss]

Because $x^2*x^3= x^5$ as Dick said. The crucial point is that it is the fifth root that is to be rationalized. You have to multiply what ever power is necessary to get a fifth power inside the fifth root.

In general to rationalize the denominator of $1/\sqrt[n]{x^m}$ you need to multiply numerator and denominator by $\sqrt[n]{x^{n-m}}$. That way, in the denominator you will have $\sqrt[n]{x^nx^{n-m}}= \sqrt[n]{x^n}= x$.

I get it now thanks..