# How do you express6sqrt7 * 3sqrt5 in simplest radical form?

Sep 3, 2015

Multiply the numbers outside the radicals together, then multiply those inside the radicals. In this case one will conclude with $18 \sqrt{35}$

#### Explanation:

$6 \sqrt{7} \cdot 3 \sqrt{5}$ (Given)

$= \left(6 \cdot 3\right) \left[\left(\sqrt{5}\right) \left(\sqrt{7}\right)\right]$ (Associative Property of Multiplication)

$= 18 \cdot \sqrt{5} \cdot \sqrt{7}$ (Multiply numbers outside radicals)

$= 18 \cdot \sqrt{35}$ (Multiply numbers inside radicals)$=$

$= 18 \sqrt{35}$