Simplify - square root of 1000a^6

$- \sqrt{1000 a^{6}}$

Step 1

Rewrite $1000 a^{6}$ as ${(10 a^{3})}^{2} \cdot 10$ .

Factor $100$ out of $1000$ .

$- \sqrt{100 (10) a^{6}}$

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

$- \sqrt{10^{2} \cdot 10 a^{6}}$

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

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

Move $10$ .

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $10$ by $- 1$ .

$- 10 a^{3} \sqrt{10}$