Algebra Examples

$\sqrt{14} (\sqrt{7} + \sqrt{2})$

Step 1

Simplify terms.

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Step 1.1

Apply the distributive property.

$\sqrt{14} \sqrt{7} + \sqrt{14} \sqrt{2}$

Step 1.2

Combine using the product rule for radicals.

$\sqrt{14 \cdot 7} + \sqrt{14} \sqrt{2}$

Step 1.3

Combine using the product rule for radicals.

$\sqrt{14 \cdot 7} + \sqrt{14 \cdot 2}$

$\sqrt{14 \cdot 7} + \sqrt{14 \cdot 2}$

Step 2

Simplify each term.

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Step 2.1

Multiply $14$ by $7$ .

$\sqrt{98} + \sqrt{14 \cdot 2}$

Step 2.2

Rewrite $98$ as $7^{2} \cdot 2$ .

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Step 2.2.1

Factor $49$ out of $98$ .

$\sqrt{49 (2)} + \sqrt{14 \cdot 2}$

Step 2.2.2

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2} \cdot 2} + \sqrt{14 \cdot 2}$

$\sqrt{7^{2} \cdot 2} + \sqrt{14 \cdot 2}$

Step 2.3

Pull terms out from under the radical.

$7 \sqrt{2} + \sqrt{14 \cdot 2}$

Step 2.4

Multiply $14$ by $2$ .

$7 \sqrt{2} + \sqrt{28}$

Step 2.5

Rewrite $28$ as $2^{2} \cdot 7$ .

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Step 2.5.1

Factor $4$ out of $28$ .

$7 \sqrt{2} + \sqrt{4 (7)}$

Step 2.5.2

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

$7 \sqrt{2} + \sqrt{2^{2} \cdot 7}$

$7 \sqrt{2} + \sqrt{2^{2} \cdot 7}$

Step 2.6

Pull terms out from under the radical.

$7 \sqrt{2} + 2 \sqrt{7}$

$7 \sqrt{2} + 2 \sqrt{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{2} + 2 \sqrt{7}$

Decimal Form:

$15.19099755 \dots$

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