Simplify the Radical Expression 3 cube root of 16-2 cube root of 54

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

Step 1

Simplify each term.

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

Factor $8$ out of $16$ .

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

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $3$ .

$6 \sqrt[3]{2} - 2 \sqrt[3]{54}$

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

Factor $27$ out of $54$ .

$6 \sqrt[3]{2} - 2 \sqrt[3]{27 (2)}$

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

$6 \sqrt[3]{2} - 2 \sqrt[3]{3^{3} \cdot 2}$

$6 \sqrt[3]{2} - 2 \sqrt[3]{3^{3} \cdot 2}$

Pull terms out from under the radical.

$6 \sqrt[3]{2} - 2 (3 \sqrt[3]{2})$

Multiply $3$ by $- 2$ .

$6 \sqrt[3]{2} - 6 \sqrt[3]{2}$

$6 \sqrt[3]{2} - 6 \sqrt[3]{2}$

Step 2

Subtract $6 \sqrt[3]{2}$ from $6 \sqrt[3]{2}$ .

$0$

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