# How do you simplify root3(-150,000)?

Apr 19, 2016

$= - 10 \sqrt[3]{150}$

#### Explanation:

First, you'll need to know this fact:, $\sqrt[n]{a b} = \sqrt[n]{a} \cdot \sqrt[n]{b}$, basically saying that you can split the big root sign into two (or even more) smaller ones.

Applying that to the question:
$\sqrt[3]{- 150000} = \sqrt[3]{150} \cdot \sqrt[3]{- 1} \cdot \sqrt[3]{1000}$

$= \sqrt[3]{150} \cdot - 1 \cdot 10$
$= - 10 \sqrt[3]{150}$