# How do you multiply (4sqrt18)(2sqrt14)?

Jun 18, 2015

$48 \sqrt{7}$

#### Explanation:

You can multiply the numbers outside the roots and them try to manipulate the arguments of the square roots:
$4 \cdot 2 \sqrt{18} \sqrt{14} =$
$= 8 \sqrt{9 \cdot 2} \sqrt{7 \cdot 2} =$
$= 8 \cdot 3 \sqrt{2} \sqrt{7 \cdot 2} =$ take one big root:

$= 24 \sqrt{2 \cdot 7 \cdot 2} =$
$= 24 \sqrt{7 \cdot 4} = 48 \sqrt{7}$