Simplify square root of 75yz^2

$\sqrt{75 y z^{2}}$

Step 1

Rewrite $75 y z^{2}$ as ${(5 z)}^{2} \cdot (3 y)$ .

Factor $25$ out of $75$ .

$\sqrt{25 (3) y z^{2}}$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} \cdot 3 y z^{2}}$

Move $y$ .

$\sqrt{5^{2} \cdot 3 z^{2} y}$

Move $3$ .

$\sqrt{5^{2} z^{2} \cdot 3 y}$

Rewrite $5^{2} z^{2}$ as ${(5 z)}^{2}$ .

$\sqrt{{(5 z)}^{2} \cdot 3 y}$

Add parentheses.

$\sqrt{{(5 z)}^{2} \cdot (3 y)}$

Step 2

Pull terms out from under the radical.

$5 z \sqrt{3 y}$