# How do you simplify 3sqrt(5c) times sqrt15^3?

Feb 22, 2018

$225 \sqrt{3 c}$

#### Explanation:

$3 \sqrt{5 c} {\sqrt{15}}^{3}$

First, we can simplify ${\sqrt{15}}^{3}$.
${\sqrt{15}}^{3} = \sqrt{15} \cdot \sqrt{15} \cdot \sqrt{15} = 15 \cdot \sqrt{15}$
$3 \cdot 15 \sqrt{5 c} \sqrt{15}$
$45 \sqrt{5 c} \sqrt{15}$

Then, we can consolidate and simplify our two irrationals.
$\sqrt{\alpha} \cdot \sqrt{\beta} = \sqrt{\alpha \beta}$
$\sqrt{5 c} \sqrt{15} = \sqrt{75 c}$
$45 \sqrt{75 c}$
$\sqrt{75 c} = \sqrt{25} \sqrt{3 c}$
$45 \cdot 5 \sqrt{3 c}$

This brings us to a simplification of the original statement:
$225 \sqrt{3 c}$