Simplify square root of xy* square root of 4xy

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

Step 1

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

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

Raise $\sqrt{x y}$ to the power of $1$ .

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

Raise $\sqrt{x y}$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

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

Step 5

Rewrite ${\sqrt{x y}}^{2}$ as $x y$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x y}$ as ${(x y)}^{\frac{1}{2}}$ .

$2 {({(x y)}^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 {(x y)}^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$2 {(x y)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 {(x y)}^{\frac{2}{2}}$

Rewrite the expression.

$2 {(x y)}^{1}$

Simplify.

$2 (x y)$

$2 x y$