Simplify cube root of 54+ cube root of 40+ cube root of 16

$\sqrt[3]{54} + \sqrt[3]{40} + \sqrt[3]{16}$

Simplify each term.

Rewrite $54$ as $3^{3} \cdot 2$ .

Factor $27$ out of $54$ .

$\sqrt[3]{27 (2)} + \sqrt[3]{40} + \sqrt[3]{16}$

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

$\sqrt[3]{3^{3} \cdot 2} + \sqrt[3]{40} + \sqrt[3]{16}$

Pull terms out from under the radical.

$3 \sqrt[3]{2} + \sqrt[3]{40} + \sqrt[3]{16}$

Rewrite $40$ as $2^{3} \cdot 5$ .

Factor $8$ out of $40$ .

$3 \sqrt[3]{2} + \sqrt[3]{8 (5)} + \sqrt[3]{16}$

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

$3 \sqrt[3]{2} + \sqrt[3]{2^{3} \cdot 5} + \sqrt[3]{16}$

Pull terms out from under the radical.

$3 \sqrt[3]{2} + 2 \sqrt[3]{5} + \sqrt[3]{16}$

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

Factor $8$ out of $16$ .

$3 \sqrt[3]{2} + 2 \sqrt[3]{5} + \sqrt[3]{8 (2)}$

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

$3 \sqrt[3]{2} + 2 \sqrt[3]{5} + \sqrt[3]{2^{3} \cdot 2}$

Pull terms out from under the radical.

$3 \sqrt[3]{2} + 2 \sqrt[3]{5} + 2 \sqrt[3]{2}$

Add $3 \sqrt[3]{2}$ and $2 \sqrt[3]{2}$ .

$5 \sqrt[3]{2} + 2 \sqrt[3]{5}$

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt[3]{2} + 2 \sqrt[3]{5}$

Decimal Form:

$9.71955714 \dots$