Simplify square root of 128c^6

$\sqrt{128 c^{6}}$

Step 1

Rewrite $128 c^{6}$ as ${(8 c^{3})}^{2} \cdot 2$ .

Factor $64$ out of $128$ .

$\sqrt{64 (2) c^{6}}$

Rewrite $64$ as $8^{2}$ .

$\sqrt{8^{2} \cdot 2 c^{6}}$

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

$\sqrt{8^{2} \cdot 2 {(c^{3})}^{2}}$

Move $2$ .

$\sqrt{8^{2} {(c^{3})}^{2} \cdot 2}$

Rewrite $8^{2} {(c^{3})}^{2}$ as ${(8 c^{3})}^{2}$ .

$\sqrt{{(8 c^{3})}^{2} \cdot 2}$

Step 2

Pull terms out from under the radical.

$8 c^{3} \sqrt{2}$