Simplify the Radical Expression 7 cube root of 2- cube root of 128

$7 \sqrt[3]{2} - \sqrt[3]{128}$

Simplify each term.

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

Factor $64$ out of $128$ .

$7 \sqrt[3]{2} - \sqrt[3]{64 (2)}$

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

$7 \sqrt[3]{2} - \sqrt[3]{4^{3} \cdot 2}$

Pull terms out from under the radical.

$7 \sqrt[3]{2} - (4 \sqrt[3]{2})$

Multiply $4$ by $- 1$ .

$7 \sqrt[3]{2} - 4 \sqrt[3]{2}$

Subtract $4 \sqrt[3]{2}$ from $7 \sqrt[3]{2}$ .

$3 \sqrt[3]{2}$

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt[3]{2}$

Decimal Form:

$3.77976314 \dots$