Simplify square root of 3x^6y

$\sqrt{3 x^{6} y}$

Rewrite $3 x^{6} y$ as ${(x^{3})}^{2} \cdot (3 y)$ .

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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