Evaluate cube root of 125/1000

$\sqrt[3]{\frac{125}{1000}}$

Step 1

Cancel the common factor of $125$ and $1000$ .

Factor $125$ out of $125$ .

$\sqrt[3]{\frac{125 (1)}{1000}}$

Cancel the common factors.

Factor $125$ out of $1000$ .

$\sqrt[3]{\frac{125 \cdot 1}{125 \cdot 8}}$

Cancel the common factor.

$\sqrt[3]{\frac{125 \cdot 1}{125 \cdot 8}}$

Rewrite the expression.

$\sqrt[3]{\frac{1}{8}}$

Step 2

Rewrite $\sqrt[3]{\frac{1}{8}}$ as $\frac{\sqrt[3]{1}}{\sqrt[3]{8}}$ .

$\frac{\sqrt[3]{1}}{\sqrt[3]{8}}$

Step 3

Any root of $1$ is $1$ .

$\frac{1}{\sqrt[3]{8}}$

Step 4

Simplify the denominator.

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

$\frac{1}{\sqrt[3]{2^{3}}}$

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

$\frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$