Simplify -3 square root of 84x^3

$- 3 \sqrt{84 x^{3}}$

Step 1

Rewrite $84 x^{3}$ as ${(2 x)}^{2} \cdot (21 x)$ .

Factor $4$ out of $84$ .

$- 3 \sqrt{4 (21) x^{3}}$

Rewrite $4$ as $2^{2}$ .

$- 3 \sqrt{2^{2} \cdot 21 x^{3}}$

Factor out $x^{2}$ .

$- 3 \sqrt{2^{2} \cdot 21 (x^{2} x)}$

Move $21$ .

$- 3 \sqrt{2^{2} x^{2} \cdot 21 x}$

Rewrite $2^{2} x^{2}$ as ${(2 x)}^{2}$ .

$- 3 \sqrt{{(2 x)}^{2} \cdot 21 x}$

Add parentheses.

$- 3 \sqrt{{(2 x)}^{2} \cdot (21 x)}$

Step 2

Pull terms out from under the radical.

$- 3 (2 x \sqrt{21 x})$

Step 3

Multiply $2$ by $- 3$ .

$- 6 x \sqrt{21 x}$