Simplify -2 square root of 147a^2b^4

$- 2 \sqrt{147 a^{2} b^{4}}$

Step 1

Rewrite $147 a^{2} b^{4}$ as ${(7 a b^{2})}^{2} \cdot 3$ .

Factor $49$ out of $147$ .

$- 2 \sqrt{49 (3) a^{2} b^{4}}$

Rewrite $49$ as $7^{2}$ .

$- 2 \sqrt{7^{2} \cdot 3 a^{2} b^{4}}$

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

$- 2 \sqrt{7^{2} \cdot 3 a^{2} {(b^{2})}^{2}}$

Move $3$ .

$- 2 \sqrt{7^{2} a^{2} {(b^{2})}^{2} \cdot 3}$

Rewrite $7^{2} a^{2} {(b^{2})}^{2}$ as ${(7 a b^{2})}^{2}$ .

$- 2 \sqrt{{(7 a b^{2})}^{2} \cdot 3}$

Step 2

Pull terms out from under the radical.

$- 2 (7 a b^{2} \sqrt{3})$

Step 3

Multiply $7$ by $- 2$ .

$- 14 a b^{2} \sqrt{3}$