Simplify the Radical Expression -3 square root of 100ab^6

$- 3 \sqrt{100 a b^{6}}$

Step 1

Rewrite $100 a b^{6}$ as ${(10 b^{3})}^{2} a$ .

Rewrite $100$ as $10^{2}$ .

$- 3 \sqrt{10^{2} a b^{6}}$

Rewrite $b^{6}$ as ${(b^{3})}^{2}$ .

$- 3 \sqrt{10^{2} a {(b^{3})}^{2}}$

Move $a$ .

$- 3 \sqrt{10^{2} {(b^{3})}^{2} a}$

Rewrite $10^{2} {(b^{3})}^{2}$ as ${(10 b^{3})}^{2}$ .

$- 3 \sqrt{{(10 b^{3})}^{2} a}$

Step 2

Pull terms out from under the radical.

$- 3 (| 10 b^{3} | \sqrt{a})$

Step 3

Remove non-negative terms from the absolute value.

$- 3 (10 | b^{3} | \sqrt{a})$

Step 4

Multiply $10$ by $- 3$ .

$- 30 | b^{3} | \sqrt{a}$