# How do you simplify (12sqrt9)/sqrt18?

Apr 17, 2016

$= 6 \sqrt{2}$

#### Explanation:

$\frac{12 \sqrt{9}}{\sqrt{18}}$

sqrt 9 = sqrt ( 3 *3 ) = color(green)(3

sqrt18 = sqrt ( 2 * 3 * 3 ) = sqrt ( 2 * 3 ^2) = color(green)( 3 sqrt2

Our expression now becomes
(12 * color(green)((3)))/ color(green)( 3 sqrt2

 = (12 * color(green)(cancel(3)))/ color(green)( cancel3 * sqrt2

$= \frac{12}{\sqrt{2}}$

Rationalising the denominator:
$= \frac{12 \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}}$

$= \frac{12 \cdot \sqrt{2}}{2}$

$= \frac{\cancel{12} \cdot \sqrt{2}}{\cancel{2}}$

$= 6 \sqrt{2}$