How do you simplify 5sqrt3 * 8sqrt2?

Sep 13, 2015

$40 \sqrt{6}$

Explanation:

Multiply the roots with the roots
and the integers with integers

$\sqrt{3}$ and $\sqrt{2}$ are the roots
$5$ and $8$ are the integers

$5 \sqrt{3} \cdot 8 \sqrt{2} \text{ }$ is the same as $\text{ } 5 \cdot 8 \cdot \sqrt{3} \cdot \sqrt{2}$

$\rightarrow 5 \cdot 8 = 40$

$\rightarrow \sqrt{3} \cdot \sqrt{2} = \sqrt{3 \cdot 2} = \sqrt{6}$

Hence, $5 \cdot 8 \cdot \sqrt{3} \cdot \sqrt{2} = \textcolor{b l u e}{40 \sqrt{6}}$