# What is sqrt24xx9sqrt3?

Sep 22, 2015

The answer is $54 \sqrt{2}$.

#### Explanation:

$\sqrt{24} \times 9 \sqrt{3}$

Simplify $\sqrt{24}$.

$\sqrt{24} = \sqrt{2 \times 2 \times 2 \times 3}$

$\sqrt{24} = \sqrt{{2}^{2} \times 2 \times 3}$

$\sqrt{{x}^{2}} = x :$$\sqrt{{2}^{2}} = 2$

$\sqrt{24} = 2 \sqrt{2 \times 3} = 2 \sqrt{6}$

Rewrite the problem.

$2 \sqrt{6} \times 9 \sqrt{3}$

Simplify.

$2 \times 9 \times \sqrt{3 \times 6} =$

$18 \sqrt{18}$

Simplify $\sqrt{18}$.

$\sqrt{18} = \sqrt{2 \times 3 \times 3} =$

$\sqrt{18} = \sqrt{2 \times {3}^{2}} =$

Rewrite the problem.

$\sqrt{18} = 3 \sqrt{2}$

Simplify.

$18 \times 3 \sqrt{2} =$

$54 \sqrt{2}$

It is $\sqrt{24} \cdot 9 \cdot \sqrt{3} = 9 \cdot \sqrt{3 \cdot {2}^{3} \cdot 3} = 9 \cdot \sqrt{{2}^{2} \cdot {3}^{2} \cdot 2} = 54 \sqrt{2}$