Algebra Examples

$\sqrt[3]{\frac{216}{729}}$

Step 1

Cancel the common factor of $216$ and $729$ .

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Step 1.1

Factor $27$ out of $216$ .

$\sqrt[3]{\frac{27 (8)}{729}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $27$ out of $729$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

Rewrite $\sqrt[3]{\frac{8}{27}}$ as $\frac{\sqrt[3]{8}}{\sqrt[3]{27}}$ .

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

Step 3

Simplify the numerator.

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Step 3.1

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

$\frac{\sqrt[3]{2^{3}}}{\sqrt[3]{27}}$

Step 3.2

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

$\frac{2}{\sqrt[3]{27}}$

Step 4

Simplify the denominator.

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Step 4.1

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

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

Step 4.2

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

$\frac{2}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$