Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

Add $1$ and $1$ .

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

Step 5

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

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Step 5.1

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

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

Step 5.2

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

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

Step 5.3

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

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

Step 5.4

Cancel the common factor of $2$ .

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Step 5.4.1

Cancel the common factor.

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

Step 5.4.2

Rewrite the expression.

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

Step 5.5

Simplify.

$2 (x y)$

$2 x y$