Basic Math Examples

$P = 2 \cdot \sqrt{8} + 2 (5 \sqrt{50})$

Step 1

Remove parentheses.

$P = 2 \cdot \sqrt{8} + 2 \cdot (5 \sqrt{50})$

Step 2

Simplify $2 \cdot \sqrt{8} + 2 \cdot (5 \sqrt{50})$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Factor $4$ out of $8$ .

$P = 2 \cdot \sqrt{4 (2)} + 2 \cdot (5 \sqrt{50})$

Step 2.1.1.2

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

$P = 2 \cdot \sqrt{2^{2} \cdot 2} + 2 \cdot (5 \sqrt{50})$

Step 2.1.2

Pull terms out from under the radical.

$P = 2 \cdot (2 \sqrt{2}) + 2 \cdot (5 \sqrt{50})$

Step 2.1.3

Multiply $2$ by $2$ .

$P = 4 \sqrt{2} + 2 \cdot (5 \sqrt{50})$

Step 2.1.4

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

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Step 2.1.4.1

Factor $25$ out of $50$ .

$P = 4 \sqrt{2} + 2 \cdot (5 \sqrt{25 (2)})$

Step 2.1.4.2

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

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

Step 2.1.5

Pull terms out from under the radical.

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

Step 2.1.6

Multiply $5$ by $5$ .

$P = 4 \sqrt{2} + 2 \cdot (25 \sqrt{2})$

Step 2.1.7

Multiply $25$ by $2$ .

$P = 4 \sqrt{2} + 50 \sqrt{2}$

Step 2.2

Add $4 \sqrt{2}$ and $50 \sqrt{2}$ .

$P = 54 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$P = 54 \sqrt{2}$

Decimal Form:

$P = 76.36753236 \dots$