# How do you simplify (6sqrt 18) / (4 sqrt 8)?

Sep 17, 2015

(6sqrt 18) / (4 sqrt 8) = color(green)( 9 / 4 = 2.25

#### Explanation:

$\frac{6 \sqrt{18}}{4 \sqrt{8}} = \frac{3 \cdot \cancel{2} \cdot \sqrt{{3}^{2} \cdot 2}}{2 \cdot \cancel{2} \cdot \sqrt{{2}^{2} \cdot 2}}$

We know that color(blue)(sqrt(a*b) = sqrta*sqrtb

$= \frac{3 \cdot \sqrt{{3}^{2}} \cdot \cancel{\sqrt{2}}}{2 \cdot \sqrt{{2}^{2}} \cdot \cancel{\sqrt{2}}}$

$= \frac{3 \cdot 3}{2 \cdot 2}$

 =color(green)( 9 / 4 = 2.25