Simplify square root of xy^5z^20

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

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

Factor out $y^{4}$ .

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

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

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

Reorder $x$ and ${(y^{2})}^{2}$ .

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

Add parentheses.

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

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

Pull terms out from under the radical.

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

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