# How do you simplify 5 square root of 8 times square root 18?

Jul 19, 2015

Use $\sqrt{a b} = \sqrt{a} \sqrt{b}$ (for $a , b \ge 0$) to find:

$5 \sqrt{8} \sqrt{18} = 60$

#### Explanation:

If $a , b \ge 0$ then $\sqrt{a b} = \sqrt{a} \sqrt{b}$

So:

$5 \sqrt{8} \sqrt{18} = 5 \sqrt{8 \cdot 18} = 5 \sqrt{144} = 5 \sqrt{{12}^{2}} = 5 \cdot 12 = 60$

Jul 19, 2015

Try and get the squares out of the root

#### Explanation:

$5 \cdot \sqrt{8} \cdot \sqrt{18} = 5 \cdot \sqrt{8 \cdot 18}$

Since $8 = {2}^{3} \mathmr{and} 18 = 2 \cdot {3}^{2}$

$= 5 \cdot \sqrt{{2}^{3} \cdot 2 \cdot {3}^{2}} = 5 \cdot \sqrt{{2}^{4} \cdot {3}^{2}}$

$= 5 \cdot \sqrt{{\left({2}^{2}\right)}^{2}} \cdot \sqrt{{3}^{2}} = 5 \cdot {2}^{2} \cdot 3 = 60$