Simplify square root of 5xy^10

$\sqrt{5 x y^{10}}$

Rewrite $5 x y^{10}$ as ${(y^{5})}^{2} \cdot (5 x)$ .

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

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

Move $x$ .

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

Reorder $5$ and ${(y^{5})}^{2}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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