# How do you multiply (3sqrt5)(2sqrt 10)?

May 3, 2015

This is easier if we first rearrange the sequence of the terms:
$\left(3 \sqrt{5}\right) \left(2 \sqrt{10}\right)$

$= \left(3 \cdot 2\right) \left(\sqrt{5} \cdot \sqrt{10}\right)$

Noting that $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$
and that sqrt(10) = sqrt(5)(sqrt(2)

We can write
$= \left(6\right) \left(5 \sqrt{2}\right)$

$= 30 \sqrt{2}$