Simplify (8 cube root of 3- cube root of 24- cube root of 81)

$(8 \sqrt[3]{3} - \sqrt[3]{24} - \sqrt[3]{81})$

Remove parentheses.

$8 \sqrt[3]{3} - \sqrt[3]{24} - \sqrt[3]{81}$

Simplify each term.

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

Factor $8$ out of $24$ .

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

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

$8 \sqrt[3]{3} - \sqrt[3]{2^{3} \cdot 3} - \sqrt[3]{81}$

Pull terms out from under the radical.

$8 \sqrt[3]{3} - (2 \sqrt[3]{3}) - \sqrt[3]{81}$

Multiply $2$ by $- 1$ .

$8 \sqrt[3]{3} - 2 \sqrt[3]{3} - \sqrt[3]{81}$

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

Factor $27$ out of $81$ .

$8 \sqrt[3]{3} - 2 \sqrt[3]{3} - \sqrt[3]{27 (3)}$

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

$8 \sqrt[3]{3} - 2 \sqrt[3]{3} - \sqrt[3]{3^{3} \cdot 3}$

Pull terms out from under the radical.

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

Multiply $3$ by $- 1$ .

$8 \sqrt[3]{3} - 2 \sqrt[3]{3} - 3 \sqrt[3]{3}$

Simplify by adding terms.

Subtract $2 \sqrt[3]{3}$ from $8 \sqrt[3]{3}$ .

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

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

$3 \sqrt[3]{3}$

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt[3]{3}$

Decimal Form:

$4.32674871 \dots$