Simplify the Radical Expression -2 square root of 48a^3b^4c^2

$- 2 \sqrt{48 a^{3} b^{4} c^{2}}$

Rewrite $48 a^{3} b^{4} c^{2}$ as ${(4 a b^{2} c)}^{2} \cdot (3 a)$ .

Factor $16$ out of $48$ .

$- 2 \sqrt{16 (3) a^{3} b^{4} c^{2}}$

Rewrite $16$ as $4^{2}$ .

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

Factor out $a^{2}$ .

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

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

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

Move $a$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Remove non-negative terms from the absolute value.

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

Multiply $4$ by $- 2$ .

$- 8 b^{2} | a c | \sqrt{3 a}$