Rationalizing Denominators w/ Cube Roots

John Whitaker

Junior Member
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May 9, 2006
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I don’t (yet) know how to illustrate the radical has an index, so I wrote it in. Perhaps I am about to learn. However,

index=4 sqrt 5x / z = index=4 sqrt 5x / index=4 sqrt z * index=4 sqrt z^3 / index=4 sqrt z^3, etc. etc. My question is, where did the exponent 3 in z^3 come from?
(I'm going to bed now, and will check in the morning.) Thank you.
John Whitaker
 
The exponent 3 is the smallest exponent needed in this case to rationalize the denominator. \(\displaystyle (5x/z)^{1/4} = (5x/z)^{1/4} \times \frac{z^{3/4}}{z^{3/4}}\).
 
I'll try to figure it out, though I don't recall anything in my text that relates to the assignment or that exponent. I'll look again.
Thanks
John Whitaker
 
You need to first answer the following question - to understand the actions suggested by royhaas:

What is meant by rationalizing the denominator?
 
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