Pre-Algebra Examples

$\sqrt[3]{\frac{81}{8}}$

Step 1

Rewrite $\sqrt[3]{\frac{81}{8}}$ as $\frac{\sqrt[3]{81}}{\sqrt[3]{8}}$ .

$\frac{\sqrt[3]{81}}{\sqrt[3]{8}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $81$ as $3^{3} \cdot 3$ .

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Step 2.1.1

Factor $27$ out of $81$ .

$\frac{\sqrt[3]{27 (3)}}{\sqrt[3]{8}}$

Step 2.1.2

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

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

Step 2.2

Pull terms out from under the radical.

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

Step 3

Simplify the denominator.

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Step 3.1

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

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

Step 3.2

Pull terms out from under the radical, assuming real numbers.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$2.16337435 \dots$