Simplify cube root of 3+ cube root of 24- cube root of 81+ cube root of 192

$\sqrt[3]{3} + \sqrt[3]{24} - \sqrt[3]{81} + \sqrt[3]{192}$

Step 1

Simplify each term.

Rewrite $24$ as $2^{3} \cdot 3$ .

Factor $8$ out of $24$ .

$\sqrt[3]{3} + \sqrt[3]{8 (3)} - \sqrt[3]{81} + \sqrt[3]{192}$

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

$\sqrt[3]{3} + \sqrt[3]{2^{3} \cdot 3} - \sqrt[3]{81} + \sqrt[3]{192}$

Pull terms out from under the radical.

$\sqrt[3]{3} + 2 \sqrt[3]{3} - \sqrt[3]{81} + \sqrt[3]{192}$

Rewrite $81$ as $3^{3} \cdot 3$ .

Factor $27$ out of $81$ .

$\sqrt[3]{3} + 2 \sqrt[3]{3} - \sqrt[3]{27 (3)} + \sqrt[3]{192}$

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

$\sqrt[3]{3} + 2 \sqrt[3]{3} - \sqrt[3]{3^{3} \cdot 3} + \sqrt[3]{192}$

Pull terms out from under the radical.

$\sqrt[3]{3} + 2 \sqrt[3]{3} - (3 \sqrt[3]{3}) + \sqrt[3]{192}$

Multiply $3$ by $- 1$ .

$\sqrt[3]{3} + 2 \sqrt[3]{3} - 3 \sqrt[3]{3} + \sqrt[3]{192}$

Rewrite $192$ as $4^{3} \cdot 3$ .

Factor $64$ out of $192$ .

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

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

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

Pull terms out from under the radical.

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

Step 2

Simplify by adding terms.

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

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

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

$0 + 4 \sqrt[3]{3}$

Add $0$ and $4 \sqrt[3]{3}$ .

$4 \sqrt[3]{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt[3]{3}$

Decimal Form:

$5.76899828 \dots$