Simplify - cube root of 320-4 cube root of 5+2 cube root of 135+2 cube root of 16

$- \sqrt[3]{320} - 4 \sqrt[3]{5} + 2 \sqrt[3]{135} + 2 \sqrt[3]{16}$

Step 1

Simplify each term.

Rewrite $320$ as $4^{3} \cdot 5$ .

Factor $64$ out of $320$ .

$- \sqrt[3]{64 (5)} - 4 \sqrt[3]{5} + 2 \sqrt[3]{135} + 2 \sqrt[3]{16}$

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

$- \sqrt[3]{4^{3} \cdot 5} - 4 \sqrt[3]{5} + 2 \sqrt[3]{135} + 2 \sqrt[3]{16}$

Pull terms out from under the radical.

$- (4 \sqrt[3]{5}) - 4 \sqrt[3]{5} + 2 \sqrt[3]{135} + 2 \sqrt[3]{16}$

Multiply $4$ by $- 1$ .

$- 4 \sqrt[3]{5} - 4 \sqrt[3]{5} + 2 \sqrt[3]{135} + 2 \sqrt[3]{16}$

Rewrite $135$ as $3^{3} \cdot 5$ .

Factor $27$ out of $135$ .

$- 4 \sqrt[3]{5} - 4 \sqrt[3]{5} + 2 \sqrt[3]{27 (5)} + 2 \sqrt[3]{16}$

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

$- 4 \sqrt[3]{5} - 4 \sqrt[3]{5} + 2 \sqrt[3]{3^{3} \cdot 5} + 2 \sqrt[3]{16}$

Pull terms out from under the radical.

$- 4 \sqrt[3]{5} - 4 \sqrt[3]{5} + 2 (3 \sqrt[3]{5}) + 2 \sqrt[3]{16}$

Multiply $3$ by $2$ .

$- 4 \sqrt[3]{5} - 4 \sqrt[3]{5} + 6 \sqrt[3]{5} + 2 \sqrt[3]{16}$

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

Factor $8$ out of $16$ .

$- 4 \sqrt[3]{5} - 4 \sqrt[3]{5} + 6 \sqrt[3]{5} + 2 \sqrt[3]{8 (2)}$

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

$- 4 \sqrt[3]{5} - 4 \sqrt[3]{5} + 6 \sqrt[3]{5} + 2 \sqrt[3]{2^{3} \cdot 2}$

Pull terms out from under the radical.

$- 4 \sqrt[3]{5} - 4 \sqrt[3]{5} + 6 \sqrt[3]{5} + 2 (2 \sqrt[3]{2})$

Multiply $2$ by $2$ .

$- 4 \sqrt[3]{5} - 4 \sqrt[3]{5} + 6 \sqrt[3]{5} + 4 \sqrt[3]{2}$

Step 2

Simplify by adding terms.

Subtract $4 \sqrt[3]{5}$ from $- 4 \sqrt[3]{5}$ .

$- 8 \sqrt[3]{5} + 6 \sqrt[3]{5} + 4 \sqrt[3]{2}$

Add $- 8 \sqrt[3]{5}$ and $6 \sqrt[3]{5}$ .

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.61973230 \dots$