# How do you simplify 9sqrt2(4sqrt6)?

May 24, 2017

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$\left(9 \cdot 4\right) \left(\sqrt{2} \cdot \sqrt{6}\right) \implies 36 \left(\sqrt{2} \cdot \sqrt{6}\right)$

Next, use this rule for multiplying radicals and it's reverse to complete the simplification:

$\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$ and $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$

$36 \left(\sqrt{2} \cdot \sqrt{6}\right) \implies 36 \sqrt{2 \cdot 6} \implies 36 \sqrt{12} \implies$

$36 \sqrt{4 \cdot 3} \implies 36 \left(\sqrt{4} \cdot \sqrt{3}\right) \implies 36 \left(2 \cdot \sqrt{3}\right) \implies$

$\left(36 \cdot 2\right) \sqrt{3} \implies$

$72 \sqrt{3}$