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

May 16, 2018

$\frac{12}{\sqrt[3]{9}} = 4 \sqrt[3]{3}$

Explanation:

$\frac{12}{\sqrt[3]{9}}$ Multiplying by ${9}^{\frac{2}{3}}$ on both numerator

and denominator we get $\frac{12 \cdot {9}^{\frac{2}{3}}}{\sqrt[3]{9} \cdot {9}^{\frac{2}{3}}}$

$= \frac{12 \cdot {9}^{\frac{2}{3}}}{{9}^{\frac{1}{3} + \frac{2}{3}}} = \frac{12 \cdot \sqrt[3]{81}}{9}$

$\frac{12 \cdot 3 \cdot \sqrt[3]{3}}{9} = 4 \sqrt[3]{3}$ [Ans]