Simplify square root of 9xy^2* square root of 4xy

$\sqrt{9 x y^{2}} \cdot \sqrt{4 x y}$

Step 1

Rewrite $9 x y^{2}$ as ${(3 y)}^{2} x$ .

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} x y^{2}} \cdot \sqrt{4 x y}$

Move $x$ .

$\sqrt{3^{2} y^{2} x} \cdot \sqrt{4 x y}$

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

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

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

Step 2

Pull terms out from under the radical.

$3 y \sqrt{x} \cdot \sqrt{4 x y}$

Step 3

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

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

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

Add parentheses.

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

Multiply $3 y \sqrt{x} (2 \sqrt{x y})$ .

Multiply $2$ by $3$ .

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

Combine using the product rule for radicals.

$6 y \sqrt{x y x}$

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

$6 y \sqrt{x^{1} x y}$

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

$6 y \sqrt{x^{1} x^{1} y}$

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

$6 y \sqrt{x^{1 + 1} y}$

Add $1$ and $1$ .

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

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

Step 6

Pull terms out from under the radical.

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

Step 7

Reorder factors in $6 y (x \sqrt{y})$ .

$6 y x \sqrt{y}$

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