# How do you simplify the square root of 21 times the square root of 24?

May 28, 2018

$= 6 \sqrt{14}$

#### Explanation:

$\sqrt{21} \cdot \sqrt{24}$

$= \sqrt{21 \cdot 24}$

Now let's break out the prime factors of each number:

=sqrt((3*7)*(2*2*2*3)

$= \sqrt{2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 7}$

$= \sqrt{{2}^{2} \cdot 2 \cdot {3}^{2} \cdot 7}$

$= 2 \cdot 3 \sqrt{2 \cdot 7}$

$= 6 \sqrt{14}$