Rationalizing the denominator that is a cube root?

Apr 2012
2
0
NV
I need help rationalizing the denominator if it is a cube root. I understand the if it is just a square root, you multiply it by itself. But im having trouble with rationalizing a cube root.
Here is the problem i need help with:
(3a)/(∛25a)
 

Plato

MHF Helper
Aug 2006
22,492
8,653
I need help rationalizing the denominator if it is a cube root. I understand the if it is just a square root, you multiply it by itself. But im having trouble with rationalizing a cube root.
Here is the problem i need help with:
(3a)/(∛25a)

\(\displaystyle \frac{3a}{\sqrt[3]{25a}}\cdot\frac{\sqrt[3]{5a^2}}{\sqrt[3]{5a^2}}=~?\)
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
\(\displaystyle \sqrt[3]{a}\sqrt[3]{a^2}= \sqrt[3]{a^3}= a\).

Or \(\displaystyle \sqrt[3]{a}\left(\sqrt[3]{a}\right)^2= (\sqrt[3]{a})^3= a\).