Simplify the Radical Expression -3 square root of 24a^4b^2c^3

$- 3 \sqrt{24 a^{4} b^{2} c^{3}}$

Rewrite $24 a^{4} b^{2} c^{3}$ as ${(2 a^{2} b c)}^{2} \cdot (6 c)$ .

Factor $4$ out of $24$ .

$- 3 \sqrt{4 (6) a^{4} b^{2} c^{3}}$

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

$- 3 \sqrt{2^{2} \cdot 6 a^{4} b^{2} c^{3}}$

Rewrite $a^{4}$ as ${(a^{2})}^{2}$ .

$- 3 \sqrt{2^{2} \cdot 6 {(a^{2})}^{2} b^{2} c^{3}}$

Factor out $c^{2}$ .

$- 3 \sqrt{2^{2} \cdot 6 {(a^{2})}^{2} b^{2} (c^{2} c)}$

Move $6$ .

$- 3 \sqrt{2^{2} {(a^{2})}^{2} b^{2} c^{2} \cdot 6 c}$

Rewrite $2^{2} {(a^{2})}^{2} b^{2} c^{2}$ as ${(2 a^{2} b c)}^{2}$ .

$- 3 \sqrt{{(2 a^{2} b c)}^{2} \cdot 6 c}$

Add parentheses.

$- 3 \sqrt{{(2 a^{2} b c)}^{2} \cdot (6 c)}$

Pull terms out from under the radical.

$- 3 (| 2 a^{2} b c | \sqrt{6 c})$

Remove non-negative terms from the absolute value.

$- 3 (2 a^{2} | b c | \sqrt{6 c})$

Multiply $2$ by $- 3$ .

$- 6 a^{2} | b c | \sqrt{6 c}$