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Simplify cube root of 8/125

$\sqrt[3]{\frac{8}{125}}$

Step 1

Rewrite

$\sqrt[3]{\frac{8}{125}}$ as

$\frac{\sqrt[3]{8}}{\sqrt[3]{125}}$ .

$\frac{\sqrt[3]{8}}{\sqrt[3]{125}}$

Step 2

Simplify the numerator.

Rewrite

$8$ as

$2^{3}$ .

$\frac{\sqrt[3]{2^{3}}}{\sqrt[3]{125}}$

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

$\frac{2}{\sqrt[3]{125}}$

Step 3

Simplify the denominator.

Rewrite

$125$ as

$5^{3}$ .

$\frac{2}{\sqrt[3]{5^{3}}}$

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

$\frac{2}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{5}$

Decimal Form:

$0.4$