How do you rationalize the denominator and simplify (-4sqrt6 - 2sqrt18 )/( sqrt3)?

Jun 17, 2016

$- 4 \sqrt{2} - 2 \sqrt{6}$

Explanation:

To Rationalize this quotient means we have to get rid of the radical from the denominator so we should multiply the numerator and denominator by $\sqrt{3}$

$\frac{- 4 \sqrt{6} - 2 \sqrt{18}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$
Knowing the property ,multiplication of two radicals that says:

$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$
$= \frac{- 4 \sqrt{6 \cdot 3} - 2 \sqrt{18 \cdot 3}}{\sqrt{3}} ^ 2$
$= \frac{- 4 \sqrt{2 \cdot 3 \cdot 3} - 2 \sqrt{2 \cdot 3 \cdot 3 \cdot 3}}{3}$
$= \frac{- 4 \cdot 3 \sqrt{2} - 2 \cdot 3 \sqrt{6}}{3}$

Simplifying by $3$
$= - 4 \sqrt{2} - 2 \sqrt{6}$