Simplify 1/5 square root of 75xy^2z^3

$\frac{1}{5} \sqrt{75 x y^{2}} z^{3}$

Step 1

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

Factor $25$ out of $75$ .

$\frac{1}{5} \cdot (\sqrt{25 (3) x y^{2}} z^{3})$

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

$\frac{1}{5} \cdot (\sqrt{5^{2} \cdot 3 x y^{2}} z^{3})$

Move $x$ .

$\frac{1}{5} \cdot (\sqrt{5^{2} \cdot 3 y^{2} x} z^{3})$

Move $3$ .

$\frac{1}{5} \cdot (\sqrt{5^{2} y^{2} \cdot 3 x} z^{3})$

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

$\frac{1}{5} \cdot (\sqrt{{(5 y)}^{2} \cdot 3 x} z^{3})$

Add parentheses.

$\frac{1}{5} \cdot (\sqrt{{(5 y)}^{2} \cdot (3 x)} z^{3})$

Step 2

Pull terms out from under the radical.

$\frac{1}{5} \cdot (5 y \sqrt{3 x} z^{3})$

Step 3

Cancel the common factor of $5$ .

Factor $5$ out of $5 y \sqrt{3 x} z^{3}$ .

$\frac{1}{5} \cdot (5 (y \sqrt{3 x} z^{3}))$

Cancel the common factor.

$\frac{1}{5} \cdot (5 (y \sqrt{3 x} z^{3}))$

Rewrite the expression.

$y \sqrt{3 x} z^{3}$