Simplify square root of 3x^10y

$\sqrt{3 x^{10} y}$

Step 1

Rewrite $3 x^{10} y$ as ${(x^{5})}^{2} \cdot (3 y)$ .

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

$\sqrt{3 {(x^{5})}^{2} y}$

Reorder $3$ and ${(x^{5})}^{2}$ .

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$x^{5} \sqrt{3 y}$