# What is the simplest radical form of -5sqrt21*(-3sqrt42)?

Jul 24, 2015

$315 \sqrt{2}$

#### Explanation:

The first thing to notice here is that you're multiplying two negative numbers, $- 5 \sqrt{21}$ and $- 3 \sqrt{42}$, so right from the start you know that the result will be positive.

Moreover, using the commutative property of multiplication, you can write

$- 5 \cdot \sqrt{21} \cdot \left(- 3 \cdot \sqrt{42}\right) = \left[- 5 \cdot \left(- 3\right)\right] \cdot \sqrt{21} \cdot \sqrt{42}$

ANother important thing to notice here is that $21$ is actually a factor of $42$

$42 = 21 \cdot 2$

This means that the expression becomes

$15 \cdot \sqrt{21} \cdot \sqrt{21 \cdot 2} = 15 \cdot {\underbrace{\sqrt{21} \cdot \sqrt{21}}}_{\textcolor{b l u e}{\text{=21}}} \cdot \sqrt{2}$

which is equivalent to

15 * color(blue)(21) * sqrt(2) = color(green)(315sqrt(2)