# How do you simplify 5 sqrt5 * 3sqrt3?

Jun 23, 2015

I found:
$15 \sqrt{15}$

#### Explanation:

Multiply the number outside AND inside the roots as:

$5 \sqrt{5} \cdot 3 \sqrt{3} = 5 \cdot 3 \sqrt{5 \cdot 3} = 15 \sqrt{15}$

Jun 23, 2015

$5 \sqrt{5} \cdot 3 \sqrt{3} = 15 \sqrt{15}$

#### Explanation:

$5 \sqrt{5}$ means $5 \cdot \sqrt{5}$
and
$3 \sqrt{3}$ means $3 \cdot \sqrt{3}$

So $5 \sqrt{5} \cdot 3 \sqrt{3}$
can be written as $5 \cdot \sqrt{5} \cdot 3 \cdot \sqrt{3}$

This can be re-arranged as
$\textcolor{w h i t e}{\text{XXXX}}$$\left(5 \cdot 3\right) \cdot \left(\sqrt{5} \cdot \sqrt{3}\right)$

and since $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$

$\textcolor{w h i t e}{\text{XXXX}}$$5 \sqrt{5} \cdot 3 \sqrt{3} = 15 \sqrt{15}$