Simplify square root of 2x^3y* square root of 6x^2y^2

$\sqrt{2 x^{3} y} \cdot \sqrt{6 x^{2} y^{2}}$

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

Factor out $x^{2}$ .

$\sqrt{2 (x^{2} x) y} \cdot \sqrt{6 x^{2} y^{2}}$

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

$\sqrt{x^{2} \cdot 2 x y} \cdot \sqrt{6 x^{2} y^{2}}$

Add parentheses.

$\sqrt{x^{2} \cdot 2 (x y)} \cdot \sqrt{6 x^{2} y^{2}}$

Add parentheses.

$\sqrt{x^{2} \cdot (2 x y)} \cdot \sqrt{6 x^{2} y^{2}}$

Pull terms out from under the radical.

$x \sqrt{2 x y} \cdot \sqrt{6 x^{2} y^{2}}$

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

Move $6$ .

$x \sqrt{2 x y} \cdot \sqrt{x^{2} y^{2} \cdot 6}$

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

$x \sqrt{2 x y} \cdot \sqrt{{(x y)}^{2} \cdot 6}$

Pull terms out from under the radical.

$x \sqrt{2 x y} \cdot (x y \sqrt{6})$

Rewrite using the commutative property of multiplication.

$\sqrt{6} x \sqrt{2 x y} (x y)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\sqrt{6} (x \cdot x) \sqrt{2 x y} y$

Multiply $x$ by $x$ .

$\sqrt{6} x^{2} \sqrt{2 x y} y$

Multiply $\sqrt{6} x^{2} \sqrt{2 x y}$ .

Combine using the product rule for radicals.

$x^{2} \sqrt{6 (2 x y)} y$

Multiply $6$ by $2$ .

$x^{2} \sqrt{12 x y} y$

Rewrite $12 x y$ as $2^{2} \cdot (3 x y)$ .

Factor $4$ out of $12$ .

$x^{2} \sqrt{4 (3) x y} y$

Rewrite $4$ as $2^{2}$ .

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

Add parentheses.

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

Add parentheses.

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

Pull terms out from under the radical.

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

Rewrite using the commutative property of multiplication.

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