Simplify square root of 80xy^2z

$\sqrt{80 x y^{2} z}$

Rewrite $80 x y^{2} z$ as ${(4 y)}^{2} \cdot (5 x z)$ .

Factor $16$ out of $80$ .

$\sqrt{16 (5) x y^{2} z}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 5 x y^{2} z}$

Move $x$ .

$\sqrt{4^{2} \cdot 5 y^{2} x z}$

Move $5$ .

$\sqrt{4^{2} y^{2} \cdot 5 x z}$

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

$\sqrt{{(4 y)}^{2} \cdot 5 x z}$

Add parentheses.

$\sqrt{{(4 y)}^{2} \cdot 5 (x z)}$

Add parentheses.

$\sqrt{{(4 y)}^{2} \cdot (5 x z)}$

Pull terms out from under the radical.

$4 y \sqrt{5 x z}$