Evaluate 5 cube root of 24+ cube root of 81

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

Step 1

Simplify each term.

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

Factor $8$ out of $24$ .

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

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $5$ .

$10 \sqrt[3]{3} + \sqrt[3]{81}$

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

Factor $27$ out of $81$ .

$10 \sqrt[3]{3} + \sqrt[3]{27 (3)}$

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

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

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

Pull terms out from under the radical.

$10 \sqrt[3]{3} + 3 \sqrt[3]{3}$

$10 \sqrt[3]{3} + 3 \sqrt[3]{3}$

Step 2

Add $10 \sqrt[3]{3}$ and $3 \sqrt[3]{3}$ .

$13 \sqrt[3]{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$13 \sqrt[3]{3}$

Decimal Form:

$18.74924441 \dots$

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