Simplify cube root of 16/27

$\sqrt[3]{\frac{16}{27}}$

Step 1

Rewrite $\sqrt[3]{\frac{16}{27}}$ as $\frac{\sqrt[3]{16}}{\sqrt[3]{27}}$ .

$\frac{\sqrt[3]{16}}{\sqrt[3]{27}}$

Step 2

Simplify the numerator.

Rewrite $16$ as $2^{3} \cdot 2$ .

Factor $8$ out of $16$ .

$\frac{\sqrt[3]{8 (2)}}{\sqrt[3]{27}}$

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

$\frac{\sqrt[3]{2^{3} \cdot 2}}{\sqrt[3]{27}}$

Pull terms out from under the radical.

$\frac{2 \sqrt[3]{2}}{\sqrt[3]{27}}$

Step 3

Simplify the denominator.

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

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

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.83994736 \dots$