Simplify square root of -50x^2yz^3

$\sqrt{- 50 x^{2} y z^{3}}$

Step 1

Rewrite $- 50 x^{2} y z^{3}$ as ${(5 x z)}^{2} \cdot (- 2 y z)$ .

Factor $25$ out of $- 50$ .

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

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

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

Factor out $z^{2}$ .

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

Move $y$ .

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

Move $- 2$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$5 x z \sqrt{- 2 y z}$