Simplify square root of 10y^10z

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

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

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

$\sqrt{10 {(y^{5})}^{2} z}$

Reorder $10$ and ${(y^{5})}^{2}$ .

$\sqrt{{(y^{5})}^{2} \cdot 10 z}$

Add parentheses.

$\sqrt{{(y^{5})}^{2} \cdot (10 z)}$

Pull terms out from under the radical.

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