Rationalizing the denominator that is a cube root?

• February 6th 2013, 03:59 PM
Hibby21
Rationalizing the denominator that is a cube root?
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)
• February 6th 2013, 04:29 PM
Plato
Re: Rationalizing the denominator that is a cube root?
Quote:

Originally Posted by Hibby21
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)

$\frac{3a}{\sqrt[3]{25a}}\cdot\frac{\sqrt[3]{5a^2}}{\sqrt[3]{5a^2}}=~?$
• February 6th 2013, 04:58 PM
HallsofIvy
Re: Rationalizing the denominator that is a cube root?
$\sqrt[3]{a}\sqrt[3]{a^2}= \sqrt[3]{a^3}= a$.

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