Trigonometry Examples

$\sqrt[3]{8 \sqrt{3^{3}}}$

Step 1

Raise $3$ to the power of $3$ .

$\sqrt[3]{8 \sqrt{27}}$

Step 2

Rewrite $27$ as $3^{2} \cdot 3$ .

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Step 2.1

Factor $9$ out of $27$ .

$\sqrt[3]{8 \sqrt{9 (3)}}$

Step 2.2

Rewrite $9$ as $3^{2}$ .

$\sqrt[3]{8 \sqrt{3^{2} \cdot 3}}$

$\sqrt[3]{8 \sqrt{3^{2} \cdot 3}}$

Step 3

Pull terms out from under the radical.

$\sqrt[3]{8 \cdot 3 \sqrt{3}}$

Step 4

Multiply $8$ by $3$ .

$\sqrt[3]{24 \sqrt{3}}$

Step 5

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

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Step 5.1

Factor $8$ out of $24$ .

$\sqrt[3]{8 (3) \sqrt{3}}$

Step 5.2

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

$\sqrt[3]{2^{3} \cdot 3 \sqrt{3}}$

Step 5.3

Add parentheses.

$\sqrt[3]{2^{3} \cdot (3 \sqrt{3})}$

$\sqrt[3]{2^{3} \cdot (3 \sqrt{3})}$

Step 6

Pull terms out from under the radical.

$2 \sqrt[3]{3 \sqrt{3}}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt[3]{3 \sqrt{3}}$

Decimal Form:

$3.46410161 \dots$

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