Evaluate cube root of 5/64

$\sqrt[3]{\frac{5}{64}}$

Step 1

Rewrite $\sqrt[3]{\frac{5}{64}}$ as $\frac{\sqrt[3]{5}}{\sqrt[3]{64}}$ .

$\frac{\sqrt[3]{5}}{\sqrt[3]{64}}$

Step 2

Simplify the denominator.

Rewrite $64$ as $4^{3}$ .

$\frac{\sqrt[3]{5}}{\sqrt[3]{4^{3}}}$

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

$\frac{\sqrt[3]{5}}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt[3]{5}}{4}$

Decimal Form:

$0.42749398 \dots$