Simplify square root of 5x^2*2y

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

Multiply $2$ by $5$ .

$\sqrt{10 x^{2} y}$

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

Reorder $10$ and $x^{2}$ .

$\sqrt{x^{2} \cdot 10 y}$

Add parentheses.

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

Pull terms out from under the radical.

$x \sqrt{10 y}$