Algebra Examples

$2 (7 \sqrt{50} + 2 \sqrt{8})$

Step 1

Simplify each term.

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Step 1.1

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 1.1.1

Factor $25$ out of $50$ .

$2 (7 \sqrt{25 (2)} + 2 \sqrt{8})$

Step 1.1.2

Rewrite $25$ as $5^{2}$ .

$2 (7 \sqrt{5^{2} \cdot 2} + 2 \sqrt{8})$

$2 (7 \sqrt{5^{2} \cdot 2} + 2 \sqrt{8})$

Step 1.2

Pull terms out from under the radical.

$2 (7 (5 \sqrt{2}) + 2 \sqrt{8})$

Step 1.3

Multiply $5$ by $7$ .

$2 (35 \sqrt{2} + 2 \sqrt{8})$

Step 1.4

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.4.1

Factor $4$ out of $8$ .

$2 (35 \sqrt{2} + 2 \sqrt{4 (2)})$

Step 1.4.2

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

$2 (35 \sqrt{2} + 2 \sqrt{2^{2} \cdot 2})$

$2 (35 \sqrt{2} + 2 \sqrt{2^{2} \cdot 2})$

Step 1.5

Pull terms out from under the radical.

$2 (35 \sqrt{2} + 2 (2 \sqrt{2}))$

Step 1.6

Multiply $2$ by $2$ .

$2 (35 \sqrt{2} + 4 \sqrt{2})$

$2 (35 \sqrt{2} + 4 \sqrt{2})$

Step 2

Simplify by adding terms.

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Step 2.1

Add $35 \sqrt{2}$ and $4 \sqrt{2}$ .

$2 (39 \sqrt{2})$

Step 2.2

Multiply $39$ by $2$ .

$78 \sqrt{2}$

$78 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$78 \sqrt{2}$

Decimal Form:

$110.30865786 \dots$

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