Finite Math Examples

$- 2 \sqrt[3]{16} - \sqrt[3]{24} - \sqrt[3]{24} - 7 \sqrt{200}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $16$ as $2^{3} \cdot 2$ .

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Step 1.1.1

Factor $8$ out of $16$ .

$- 2 \sqrt[3]{8 (2)} - \sqrt[3]{24} - \sqrt[3]{24} - 7 \sqrt{200}$

Step 1.1.2

Rewrite $8$ as $2^{3}$ .

$- 2 \sqrt[3]{2^{3} \cdot 2} - \sqrt[3]{24} - \sqrt[3]{24} - 7 \sqrt{200}$

Step 1.2

Pull terms out from under the radical.

$- 2 (2 \sqrt[3]{2}) - \sqrt[3]{24} - \sqrt[3]{24} - 7 \sqrt{200}$

Step 1.3

Multiply $2$ by $- 2$ .

$- 4 \sqrt[3]{2} - \sqrt[3]{24} - \sqrt[3]{24} - 7 \sqrt{200}$

Step 1.4

Rewrite $24$ as $2^{3} \cdot 3$ .

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Step 1.4.1

Factor $8$ out of $24$ .

$- 4 \sqrt[3]{2} - \sqrt[3]{8 (3)} - \sqrt[3]{24} - 7 \sqrt{200}$

Step 1.4.2

Rewrite $8$ as $2^{3}$ .

$- 4 \sqrt[3]{2} - \sqrt[3]{2^{3} \cdot 3} - \sqrt[3]{24} - 7 \sqrt{200}$

Step 1.5

Pull terms out from under the radical.

$- 4 \sqrt[3]{2} - (2 \sqrt[3]{3}) - \sqrt[3]{24} - 7 \sqrt{200}$

Step 1.6

Multiply $2$ by $- 1$ .

$- 4 \sqrt[3]{2} - 2 \sqrt[3]{3} - \sqrt[3]{24} - 7 \sqrt{200}$

Step 1.7

Rewrite $24$ as $2^{3} \cdot 3$ .

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Step 1.7.1

Factor $8$ out of $24$ .

$- 4 \sqrt[3]{2} - 2 \sqrt[3]{3} - \sqrt[3]{8 (3)} - 7 \sqrt{200}$

Step 1.7.2

Rewrite $8$ as $2^{3}$ .

$- 4 \sqrt[3]{2} - 2 \sqrt[3]{3} - \sqrt[3]{2^{3} \cdot 3} - 7 \sqrt{200}$

Step 1.8

Pull terms out from under the radical.

$- 4 \sqrt[3]{2} - 2 \sqrt[3]{3} - (2 \sqrt[3]{3}) - 7 \sqrt{200}$

Step 1.9

Multiply $2$ by $- 1$ .

$- 4 \sqrt[3]{2} - 2 \sqrt[3]{3} - 2 \sqrt[3]{3} - 7 \sqrt{200}$

Step 1.10

Rewrite $200$ as $10^{2} \cdot 2$ .

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Step 1.10.1

Factor $100$ out of $200$ .

$- 4 \sqrt[3]{2} - 2 \sqrt[3]{3} - 2 \sqrt[3]{3} - 7 \sqrt{100 (2)}$

Step 1.10.2

Rewrite $100$ as $10^{2}$ .

$- 4 \sqrt[3]{2} - 2 \sqrt[3]{3} - 2 \sqrt[3]{3} - 7 \sqrt{10^{2} \cdot 2}$

Step 1.11

Pull terms out from under the radical.

$- 4 \sqrt[3]{2} - 2 \sqrt[3]{3} - 2 \sqrt[3]{3} - 7 (10 \sqrt{2})$

Step 1.12

Multiply $10$ by $- 7$ .

$- 4 \sqrt[3]{2} - 2 \sqrt[3]{3} - 2 \sqrt[3]{3} - 70 \sqrt{2}$

Step 2

Subtract $2 \sqrt[3]{3}$ from $- 2 \sqrt[3]{3}$ .

$- 4 \sqrt[3]{2} - 4 \sqrt[3]{3} - 70 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 4 \sqrt[3]{2} - 4 \sqrt[3]{3} - 70 \sqrt{2}$

Decimal Form:

$- 109.80363184 \dots$