Evaluate cube root of 216/343

$\sqrt[3]{\frac{216}{343}}$

Step 1

Rewrite $\sqrt[3]{\frac{216}{343}}$ as $\frac{\sqrt[3]{216}}{\sqrt[3]{343}}$ .

$\frac{\sqrt[3]{216}}{\sqrt[3]{343}}$

Step 2

Simplify the numerator.

Rewrite $216$ as $6^{3}$ .

$\frac{\sqrt[3]{6^{3}}}{\sqrt[3]{343}}$

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

$\frac{6}{\sqrt[3]{343}}$

Step 3

Simplify the denominator.

Rewrite $343$ as $7^{3}$ .

$\frac{6}{\sqrt[3]{7^{3}}}$

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

$\frac{6}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{6}{7}$

Decimal Form:

$0.\overline{857142}$