Algebra Examples

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

Step 1

Apply the distributive property.

$\sqrt{2 x} \sqrt{2} + \sqrt{2 x} \sqrt{x}$

Step 2

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

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Step 2.1

Combine using the product rule for radicals.

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

Step 2.2

Multiply $2$ by $2$ .

$\sqrt{4 x} + \sqrt{2 x} \sqrt{x}$

$\sqrt{4 x} + \sqrt{2 x} \sqrt{x}$

Step 3

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

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Step 3.1

Combine using the product rule for radicals.

$\sqrt{4 x} + \sqrt{2 x \cdot x}$

Step 3.2

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

$\sqrt{4 x} + \sqrt{2 (x^{1} x)}$

Step 3.3

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

$\sqrt{4 x} + \sqrt{2 (x^{1} x^{1})}$

Step 3.4

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

$\sqrt{4 x} + \sqrt{2 x^{1 + 1}}$

Step 3.5

Add $1$ and $1$ .

$\sqrt{4 x} + \sqrt{2 x^{2}}$

$\sqrt{4 x} + \sqrt{2 x^{2}}$

Step 4

Simplify each term.

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Step 4.1

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

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

Step 4.2

Pull terms out from under the radical.

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

Step 4.3

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

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

Step 4.4

Pull terms out from under the radical.

$2 \sqrt{x} + x \sqrt{2}$

$2 \sqrt{x} + x \sqrt{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$