# How do you multiply (2sqrt21)(3sqrt6)?

Jun 19, 2015

$\left(2 \sqrt{21}\right) \left(3 \sqrt{6}\right) = 6 \sqrt{21 \cdot 6} = 6 \sqrt{9 \cdot 14} = 18 \sqrt{14}$

#### Explanation:

$\left(2 \sqrt{21}\right) \left(3 \sqrt{6}\right)$

$= 2 \cdot \sqrt{21} \cdot 3 \cdot \sqrt{6}$

$= 2 \cdot 3 \cdot \sqrt{21} \cdot \sqrt{6}$

$= 6 \cdot \sqrt{21 \cdot 6}$

$= 6 \cdot \sqrt{9 \cdot 14}$

$= 6 \cdot \sqrt{9} \cdot \sqrt{14}$

$= 6 \cdot 3 \cdot \sqrt{14}$

$= 18 \sqrt{14}$

If $a , b > 0$ then $\sqrt{a b} = \sqrt{a} \sqrt{b}$