Evaluate 7 cube root of 24-5 cube root of 81+3 cube root of 3000

$7 \sqrt[3]{24} - 5 \sqrt[3]{81} + 3 \sqrt[3]{3000}$

Step 1

Simplify each term.

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

Factor $8$ out of $24$ .

$7 \sqrt[3]{8 (3)} - 5 \sqrt[3]{81} + 3 \sqrt[3]{3000}$

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

$7 \sqrt[3]{2^{3} \cdot 3} - 5 \sqrt[3]{81} + 3 \sqrt[3]{3000}$

Pull terms out from under the radical.

$7 (2 \sqrt[3]{3}) - 5 \sqrt[3]{81} + 3 \sqrt[3]{3000}$

Multiply $2$ by $7$ .

$14 \sqrt[3]{3} - 5 \sqrt[3]{81} + 3 \sqrt[3]{3000}$

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

Factor $27$ out of $81$ .

$14 \sqrt[3]{3} - 5 \sqrt[3]{27 (3)} + 3 \sqrt[3]{3000}$

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

$14 \sqrt[3]{3} - 5 \sqrt[3]{3^{3} \cdot 3} + 3 \sqrt[3]{3000}$

Pull terms out from under the radical.

$14 \sqrt[3]{3} - 5 (3 \sqrt[3]{3}) + 3 \sqrt[3]{3000}$

Multiply $3$ by $- 5$ .

$14 \sqrt[3]{3} - 15 \sqrt[3]{3} + 3 \sqrt[3]{3000}$

Rewrite $3000$ as $10^{3} \cdot 3$ .

Factor $1000$ out of $3000$ .

$14 \sqrt[3]{3} - 15 \sqrt[3]{3} + 3 \sqrt[3]{1000 (3)}$

Rewrite $1000$ as $10^{3}$ .

$14 \sqrt[3]{3} - 15 \sqrt[3]{3} + 3 \sqrt[3]{10^{3} \cdot 3}$

Pull terms out from under the radical.

$14 \sqrt[3]{3} - 15 \sqrt[3]{3} + 3 (10 \sqrt[3]{3})$

Multiply $10$ by $3$ .

$14 \sqrt[3]{3} - 15 \sqrt[3]{3} + 30 \sqrt[3]{3}$

Step 2

Simplify by adding terms.

Subtract $15 \sqrt[3]{3}$ from $14 \sqrt[3]{3}$ .

$- \sqrt[3]{3} + 30 \sqrt[3]{3}$

Add $- \sqrt[3]{3}$ and $30 \sqrt[3]{3}$ .

$29 \sqrt[3]{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$29 \sqrt[3]{3}$

Decimal Form:

$41.82523753 \dots$