Simplify square root of 18k^6

$\sqrt{18 k^{6}}$

Step 1

Rewrite $18 k^{6}$ as ${(3 k^{3})}^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$\sqrt{9 (2) k^{6}}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 2 k^{6}}$

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

$\sqrt{3^{2} \cdot 2 {(k^{3})}^{2}}$

Move $2$ .

$\sqrt{3^{2} {(k^{3})}^{2} \cdot 2}$

Rewrite $3^{2} {(k^{3})}^{2}$ as ${(3 k^{3})}^{2}$ .

$\sqrt{{(3 k^{3})}^{2} \cdot 2}$

Step 2

Pull terms out from under the radical.

$3 k^{3} \sqrt{2}$