SOLUTION: My homework says to rationalize the denominator. I've tried another problem similar to this and I ended up getting it wrong. This is another one I'm stuck on. Cube root of 35 over

Algebra ->  Radicals -> SOLUTION: My homework says to rationalize the denominator. I've tried another problem similar to this and I ended up getting it wrong. This is another one I'm stuck on. Cube root of 35 over       Log On


   

Question 532580: My homework says to rationalize the denominator. I've tried another problem similar to this and I ended up getting it wrong. This is another one I'm stuck on. Cube root of 35 over the cube root of 21. I thought you had to break the top as cube roots of 5 and 7 and break the bottom as cube roots of 3 and 7 and cancel out, then multiply the top and bottom by the cube root of three. Is that the correct way to rationalize? Please and thank you!
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Cube root of 35 over the cube root of 21
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Multiply numerator and denomator by cbrt(21^2) to get:
----
= cbrt(35*21^2)/cbrt(21^3)
----
= cbrt(7^3*5*3^2)/21
----
= (7/21)*cbrt(45)
---
= (1/3)cbrt(45)
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Cheers,
Stan H.
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Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Cube root of 35 over the cube root of 21.
----------------
root%283%2C35%29%2Froot%283%2C21%29+=+root%283%2C35%2F21%29+=+root%283%2C5%2F3%29
= root%283%2C45%2F27%29+=+root%283%2C45%29%2F3