Simplify 2 cube root of 16+5 cube root of 54- cube root of 250+1/2 cube root of 128

$2 \sqrt[3]{16} + 5 \sqrt[3]{54} - \sqrt[3]{250} + \frac{1}{2} \sqrt[3]{128}$

Step 1

Simplify each term.

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

Factor $8$ out of $16$ .

$2 \sqrt[3]{8 (2)} + 5 \sqrt[3]{54} - \sqrt[3]{250} + \frac{1}{2} \cdot \sqrt[3]{128}$

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

$2 \sqrt[3]{2^{3} \cdot 2} + 5 \sqrt[3]{54} - \sqrt[3]{250} + \frac{1}{2} \cdot \sqrt[3]{128}$

Pull terms out from under the radical.

$2 (2 \sqrt[3]{2}) + 5 \sqrt[3]{54} - \sqrt[3]{250} + \frac{1}{2} \cdot \sqrt[3]{128}$

Multiply $2$ by $2$ .

$4 \sqrt[3]{2} + 5 \sqrt[3]{54} - \sqrt[3]{250} + \frac{1}{2} \cdot \sqrt[3]{128}$

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

Factor $27$ out of $54$ .

$4 \sqrt[3]{2} + 5 \sqrt[3]{27 (2)} - \sqrt[3]{250} + \frac{1}{2} \cdot \sqrt[3]{128}$

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

$4 \sqrt[3]{2} + 5 \sqrt[3]{3^{3} \cdot 2} - \sqrt[3]{250} + \frac{1}{2} \cdot \sqrt[3]{128}$

Pull terms out from under the radical.

$4 \sqrt[3]{2} + 5 (3 \sqrt[3]{2}) - \sqrt[3]{250} + \frac{1}{2} \cdot \sqrt[3]{128}$

Multiply $3$ by $5$ .

$4 \sqrt[3]{2} + 15 \sqrt[3]{2} - \sqrt[3]{250} + \frac{1}{2} \cdot \sqrt[3]{128}$

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

Factor $125$ out of $250$ .

$4 \sqrt[3]{2} + 15 \sqrt[3]{2} - \sqrt[3]{125 (2)} + \frac{1}{2} \cdot \sqrt[3]{128}$

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

$4 \sqrt[3]{2} + 15 \sqrt[3]{2} - \sqrt[3]{5^{3} \cdot 2} + \frac{1}{2} \cdot \sqrt[3]{128}$

Pull terms out from under the radical.

$4 \sqrt[3]{2} + 15 \sqrt[3]{2} - (5 \sqrt[3]{2}) + \frac{1}{2} \cdot \sqrt[3]{128}$

Multiply $5$ by $- 1$ .

$4 \sqrt[3]{2} + 15 \sqrt[3]{2} - 5 \sqrt[3]{2} + \frac{1}{2} \cdot \sqrt[3]{128}$

Rewrite $128$ as $4^{3} \cdot 2$ .

Factor $64$ out of $128$ .

$4 \sqrt[3]{2} + 15 \sqrt[3]{2} - 5 \sqrt[3]{2} + \frac{1}{2} \cdot \sqrt[3]{64 (2)}$

Rewrite $64$ as $4^{3}$ .

$4 \sqrt[3]{2} + 15 \sqrt[3]{2} - 5 \sqrt[3]{2} + \frac{1}{2} \cdot \sqrt[3]{4^{3} \cdot 2}$

Pull terms out from under the radical.

$4 \sqrt[3]{2} + 15 \sqrt[3]{2} - 5 \sqrt[3]{2} + \frac{1}{2} \cdot (4 \sqrt[3]{2})$

Cancel the common factor of $2$ .

Factor $2$ out of $4 \sqrt[3]{2}$ .

$4 \sqrt[3]{2} + 15 \sqrt[3]{2} - 5 \sqrt[3]{2} + \frac{1}{2} \cdot (2 (2 \sqrt[3]{2}))$

Cancel the common factor.

$4 \sqrt[3]{2} + 15 \sqrt[3]{2} - 5 \sqrt[3]{2} + \frac{1}{2} \cdot (2 (2 \sqrt[3]{2}))$

Rewrite the expression.

$4 \sqrt[3]{2} + 15 \sqrt[3]{2} - 5 \sqrt[3]{2} + 2 \sqrt[3]{2}$

Step 2

Simplify by adding terms.

Add $4 \sqrt[3]{2}$ and $15 \sqrt[3]{2}$ .

$19 \sqrt[3]{2} - 5 \sqrt[3]{2} + 2 \sqrt[3]{2}$

Subtract $5 \sqrt[3]{2}$ from $19 \sqrt[3]{2}$ .

$14 \sqrt[3]{2} + 2 \sqrt[3]{2}$

Add $14 \sqrt[3]{2}$ and $2 \sqrt[3]{2}$ .

$16 \sqrt[3]{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$16 \sqrt[3]{2}$

Decimal Form:

$20.15873679 \dots$

Simplify 2 cube root of 16+5 cube root of 54- cube root of 250+1/2 cube root of 128

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