# How do you simplify 3/root3(6) ?

Jul 11, 2018

$\sqrt[3]{\frac{9}{2}}$

#### Explanation:

we have
$\frac{3}{\sqrt[3]{6}} = \frac{3}{6} ^ \left(\frac{1}{3}\right) \cdot 3 \cdot {6}^{- \frac{1}{3}} = 3 \cdot {3}^{- \frac{1}{3}} \cdot {2}^{- \frac{1}{3}} = {3}^{\frac{2}{3}} / {2}^{\frac{1}{3}} = \sqrt[3]{\frac{9}{2}}$

$\setminus \sqrt[3]{\frac{9}{2}}$

#### Explanation:

Given that

$\frac{3}{\setminus} \sqrt[3]{6}$

$= \setminus \frac{\setminus \sqrt[3]{{3}^{3}}}{\setminus \sqrt[3]{6}}$

$= \setminus \sqrt[3]{\setminus \frac{{3}^{3}}{6}}$

$= \setminus \sqrt[3]{\frac{27}{6}}$

$= \setminus \sqrt[3]{\frac{9}{2}}$

Jul 11, 2018

$\frac{3}{\sqrt[3]{6}} = \frac{\sqrt[3]{36}}{2}$

#### Explanation:

To rationalise the denominator, we can proceed as follows:

$\frac{3}{\sqrt[3]{6}} = \frac{3 \cdot \sqrt[3]{{6}^{2}}}{\sqrt[3]{6} \sqrt[3]{{6}^{2}}}$

$\textcolor{w h i t e}{\frac{3}{\sqrt[3]{6}}} = \frac{3 \sqrt[3]{36}}{\sqrt[3]{{6}^{3}}}$

$\textcolor{w h i t e}{\frac{3}{\sqrt[3]{6}}} = \frac{3 \sqrt[3]{36}}{6}$

$\textcolor{w h i t e}{\frac{3}{\sqrt[3]{6}}} = \frac{\sqrt[3]{36}}{2}$