Trigonometry Examples

$5 \sqrt[3]{40} + \sqrt[3]{135}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $40$ as $2^{3} \cdot 5$ .

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Step 1.1.1

Factor $8$ out of $40$ .

$5 \sqrt[3]{8 (5)} + \sqrt[3]{135}$

Step 1.1.2

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

$5 \sqrt[3]{2^{3} \cdot 5} + \sqrt[3]{135}$

$5 \sqrt[3]{2^{3} \cdot 5} + \sqrt[3]{135}$

Step 1.2

Pull terms out from under the radical.

$5 (2 \sqrt[3]{5}) + \sqrt[3]{135}$

Step 1.3

Multiply $2$ by $5$ .

$10 \sqrt[3]{5} + \sqrt[3]{135}$

Step 1.4

Rewrite $135$ as $3^{3} \cdot 5$ .

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Step 1.4.1

Factor $27$ out of $135$ .

$10 \sqrt[3]{5} + \sqrt[3]{27 (5)}$

Step 1.4.2

Rewrite $27$ as $3^{3}$ .

$10 \sqrt[3]{5} + \sqrt[3]{3^{3} \cdot 5}$

$10 \sqrt[3]{5} + \sqrt[3]{3^{3} \cdot 5}$

Step 1.5

Pull terms out from under the radical.

$10 \sqrt[3]{5} + 3 \sqrt[3]{5}$

$10 \sqrt[3]{5} + 3 \sqrt[3]{5}$

Step 2

Add $10 \sqrt[3]{5}$ and $3 \sqrt[3]{5}$ .

$13 \sqrt[3]{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$13 \sqrt[3]{5}$

Decimal Form:

$22.22968730 \dots$

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