Simplify the Radical Expression square root of xy^5z^20

$\sqrt{x y^{5} z^{20}}$

Step 1

Rewrite $x y^{5} z^{20}$ as ${(y^{2} z^{10})}^{2} (x y)$ .

Factor out $y^{4}$ .

$\sqrt{x (y^{4} y) z^{20}}$

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

$\sqrt{x ({(y^{2})}^{2} y) z^{20}}$

Rewrite $z^{20}$ as ${(z^{10})}^{2}$ .

$\sqrt{x ({(y^{2})}^{2} y) {(z^{10})}^{2}}$

Move $y$ .

$\sqrt{x ({(y^{2})}^{2}) {(z^{10})}^{2} y}$

Move $x$ .

$\sqrt{({(y^{2})}^{2}) {(z^{10})}^{2} x y}$

Rewrite $({(y^{2})}^{2}) {(z^{10})}^{2}$ as ${(y^{2} z^{10})}^{2}$ .

$\sqrt{{(y^{2} z^{10})}^{2} x y}$

Add parentheses.

$\sqrt{{(y^{2} z^{10})}^{2} (x y)}$

Step 2

Pull terms out from under the radical.

$| y^{2} z^{10} | \sqrt{x y}$

Step 3

Remove non-negative terms from the absolute value.

$y^{2} z^{10} \sqrt{x y}$