Finite Math Examples

$\frac{10 \sqrt[3]{960}}{35 \sqrt[3]{5}}$

Step 1

Cancel the common factor of $10$ and $35$ .

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Step 1.1

Factor $5$ out of $10 \sqrt[3]{960}$ .

$\frac{5 (2 \sqrt[3]{960})}{35 \sqrt[3]{5}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $5$ out of $35 \sqrt[3]{5}$ .

$\frac{5 (2 \sqrt[3]{960})}{5 (7 \sqrt[3]{5})}$

Step 1.2.2

Cancel the common factor.

$\frac{5 (2 \sqrt[3]{960})}{5 (7 \sqrt[3]{5})}$

Step 1.2.3

Rewrite the expression.

$\frac{2 \sqrt[3]{960}}{7 \sqrt[3]{5}}$

$\frac{2 \sqrt[3]{960}}{7 \sqrt[3]{5}}$

$\frac{2 \sqrt[3]{960}}{7 \sqrt[3]{5}}$

Step 2

Combine $\sqrt[3]{960}$ and $\sqrt[3]{5}$ into a single radical.

$\frac{2 \sqrt[3]{\frac{960}{5}}}{7}$

Step 3

Cancel the common factor of $960$ and $5$ .

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Step 3.1

Factor $5$ out of $960$ .

$\frac{2 \sqrt[3]{\frac{5 \cdot 192}{5}}}{7}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $5$ out of $5$ .

$\frac{2 \sqrt[3]{\frac{5 \cdot 192}{5 (1)}}}{7}$

Step 3.2.2

Cancel the common factor.

$\frac{2 \sqrt[3]{\frac{5 \cdot 192}{5 \cdot 1}}}{7}$

Step 3.2.3

Rewrite the expression.

$\frac{2 \sqrt[3]{\frac{192}{1}}}{7}$

Step 3.2.4

Divide $192$ by $1$ .

$\frac{2 \sqrt[3]{192}}{7}$

$\frac{2 \sqrt[3]{192}}{7}$

$\frac{2 \sqrt[3]{192}}{7}$

Step 4

Simplify the numerator.

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Step 4.1

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

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Step 4.1.1

Factor $64$ out of $192$ .

$\frac{2 \sqrt[3]{64 (3)}}{7}$

Step 4.1.2

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

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

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

Step 4.2

Pull terms out from under the radical.

$\frac{2 \cdot 4 \sqrt[3]{3}}{7}$

Step 4.3

Multiply $2$ by $4$ .

$\frac{8 \sqrt[3]{3}}{7}$

$\frac{8 \sqrt[3]{3}}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{8 \sqrt[3]{3}}{7}$

Decimal Form:

$1.64828522 \dots$

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