Simplify square root of 72z^5

$\sqrt{72 z^{5}}$

Step 1

Rewrite $72 z^{5}$ as ${(6 z^{2})}^{2} \cdot (2 z)$ .

Factor $36$ out of $72$ .

$\sqrt{36 (2) z^{5}}$

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} \cdot 2 z^{5}}$

Factor out $z^{4}$ .

$\sqrt{6^{2} \cdot 2 (z^{4} z)}$

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

$\sqrt{6^{2} \cdot 2 ({(z^{2})}^{2} z)}$

Move $2$ .

$\sqrt{6^{2} {(z^{2})}^{2} \cdot 2 z}$

Rewrite $6^{2} {(z^{2})}^{2}$ as ${(6 z^{2})}^{2}$ .

$\sqrt{{(6 z^{2})}^{2} \cdot 2 z}$

Add parentheses.

$\sqrt{{(6 z^{2})}^{2} \cdot (2 z)}$

Step 2

Pull terms out from under the radical.

$6 z^{2} \sqrt{2 z}$