Basic Math Examples

$5 \sqrt[3]{24} - \sqrt[3]{192}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $8$ out of $24$ .

$5 \sqrt[3]{8 (3)} - \sqrt[3]{192}$

Step 1.1.2

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

$5 \sqrt[3]{2^{3} \cdot 3} - \sqrt[3]{192}$

$5 \sqrt[3]{2^{3} \cdot 3} - \sqrt[3]{192}$

Step 1.2

Pull terms out from under the radical.

$5 (2 \sqrt[3]{3}) - \sqrt[3]{192}$

Step 1.3

Multiply $2$ by $5$ .

$10 \sqrt[3]{3} - \sqrt[3]{192}$

Step 1.4

Rewrite $192$ as $4^{3} \cdot 3$ .

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Step 1.4.1

Factor $64$ out of $192$ .

$10 \sqrt[3]{3} - \sqrt[3]{64 (3)}$

Step 1.4.2

Rewrite $64$ as $4^{3}$ .

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

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

Step 1.5

Pull terms out from under the radical.

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

Step 1.6

Multiply $4$ by $- 1$ .

$10 \sqrt[3]{3} - 4 \sqrt[3]{3}$

$10 \sqrt[3]{3} - 4 \sqrt[3]{3}$

Step 2

Subtract $4 \sqrt[3]{3}$ from $10 \sqrt[3]{3}$ .

$6 \sqrt[3]{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt[3]{3}$

Decimal Form:

$8.65349742 \dots$

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