Simplify cube root of 16-3 cube root of 54+2 cube root of 250

$\sqrt[3]{16} - 3 \sqrt[3]{54} + 2 \sqrt[3]{250}$

Simplify each term.

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

Factor $8$ out of $16$ .

$\sqrt[3]{8 (2)} - 3 \sqrt[3]{54} + 2 \sqrt[3]{250}$

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

$\sqrt[3]{2^{3} \cdot 2} - 3 \sqrt[3]{54} + 2 \sqrt[3]{250}$

Pull terms out from under the radical.

$2 \sqrt[3]{2} - 3 \sqrt[3]{54} + 2 \sqrt[3]{250}$

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

Factor $27$ out of $54$ .

$2 \sqrt[3]{2} - 3 \sqrt[3]{27 (2)} + 2 \sqrt[3]{250}$

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

$2 \sqrt[3]{2} - 3 \sqrt[3]{3^{3} \cdot 2} + 2 \sqrt[3]{250}$

Pull terms out from under the radical.

$2 \sqrt[3]{2} - 3 (3 \sqrt[3]{2}) + 2 \sqrt[3]{250}$

Multiply $3$ by $- 3$ .

$2 \sqrt[3]{2} - 9 \sqrt[3]{2} + 2 \sqrt[3]{250}$

Rewrite $250$ as $5^{3} \cdot 2$ .

Factor $125$ out of $250$ .

$2 \sqrt[3]{2} - 9 \sqrt[3]{2} + 2 \sqrt[3]{125 (2)}$

Rewrite $125$ as $5^{3}$ .

$2 \sqrt[3]{2} - 9 \sqrt[3]{2} + 2 \sqrt[3]{5^{3} \cdot 2}$

Pull terms out from under the radical.

$2 \sqrt[3]{2} - 9 \sqrt[3]{2} + 2 (5 \sqrt[3]{2})$

Multiply $5$ by $2$ .

$2 \sqrt[3]{2} - 9 \sqrt[3]{2} + 10 \sqrt[3]{2}$

Simplify by adding terms.

Subtract $9 \sqrt[3]{2}$ from $2 \sqrt[3]{2}$ .

$- 7 \sqrt[3]{2} + 10 \sqrt[3]{2}$

Add $- 7 \sqrt[3]{2}$ and $10 \sqrt[3]{2}$ .

$3 \sqrt[3]{2}$

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt[3]{2}$

Decimal Form:

$3.77976314 \dots$