Algebra Examples

$\sqrt{2} (\sqrt{10} + \sqrt{4})$

Step 1

Simplify each term.

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Step 1.1

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

$\sqrt{2} (\sqrt{10} + \sqrt{2^{2}})$

Step 1.2

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt{2} (\sqrt{10} + 2)$

$\sqrt{2} (\sqrt{10} + 2)$

Step 2

Simplify terms.

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Step 2.1

Apply the distributive property.

$\sqrt{2} \sqrt{10} + \sqrt{2} \cdot 2$

Step 2.2

Combine using the product rule for radicals.

$\sqrt{2 \cdot 10} + \sqrt{2} \cdot 2$

Step 2.3

Move $2$ to the left of $\sqrt{2}$ .

$\sqrt{2 \cdot 10} + 2 \cdot \sqrt{2}$

$\sqrt{2 \cdot 10} + 2 \cdot \sqrt{2}$

Step 3

Simplify each term.

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Step 3.1

Multiply $2$ by $10$ .

$\sqrt{20} + 2 \cdot \sqrt{2}$

Step 3.2

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 3.2.1

Factor $4$ out of $20$ .

$\sqrt{4 (5)} + 2 \cdot \sqrt{2}$

Step 3.2.2

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

$\sqrt{2^{2} \cdot 5} + 2 \cdot \sqrt{2}$

$\sqrt{2^{2} \cdot 5} + 2 \cdot \sqrt{2}$

Step 3.3

Pull terms out from under the radical.

$2 \sqrt{5} + 2 \sqrt{2}$

$2 \sqrt{5} + 2 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{5} + 2 \sqrt{2}$

Decimal Form:

$7.30056307 \dots$

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