Evaluate cube root of 3 3/8

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

Step 1

Convert $3 \frac{3}{8}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

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

Add $3$ and $\frac{3}{8}$ .

To write $3$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

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

Combine $3$ and $\frac{8}{8}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $8$ .

$\sqrt[3]{\frac{24 + 3}{8}}$

Add $24$ and $3$ .

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

Step 2

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

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

Step 3

Simplify the numerator.

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

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

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

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

Step 4

Simplify the denominator.

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

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

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

$\frac{3}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$