# How do you rationalize the denominator and simplify 12/root3(9)?

Apr 16, 2018

$4 \sqrt[3]{3}$

#### Explanation:

$\frac{12}{\sqrt[3]{9}}$

To rationalize, multiply the expression by $\frac{\sqrt[3]{{9}^{2}}}{\sqrt[3]{{9}^{2}}}$:

$\frac{12}{\sqrt[3]{9}} \cdot \frac{\sqrt[3]{{9}^{2}}}{\sqrt[3]{{9}^{2}}} =$

$\frac{12 \left(\sqrt[3]{{9}^{2}}\right)}{\sqrt[3]{{9}^{3}}} =$

$\frac{12 \left(\sqrt[3]{81}\right)}{9} =$

$\frac{12 \left(\sqrt[3]{27 \cdot 3}\right)}{9} =$

$\frac{12 \cdot 3 \left(\sqrt[3]{3}\right)}{9} =$

$\frac{36 \left(\sqrt[3]{3}\right)}{9} =$

$4 \sqrt[3]{3}$