Simplify square root of 4xy^2* square root of xy

$\sqrt{4 x y^{2}} \cdot \sqrt{x y}$

Step 1

Rewrite $4 x y^{2}$ as ${(2 y)}^{2} x$ .

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

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

Move $x$ .

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

Combine using the product rule for radicals.

$2 y \sqrt{x y x}$

Raise $x$ to the power of $1$ .

$2 y \sqrt{x^{1} x y}$

Raise $x$ to the power of $1$ .

$2 y \sqrt{x^{1} x^{1} y}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 y \sqrt{x^{1 + 1} y}$

Add $1$ and $1$ .

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

Step 4

Pull terms out from under the radical.

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

Step 5

Reorder factors in $2 y (x \sqrt{y})$ .

$2 y x \sqrt{y}$