Simplify cube root of 3(5 cube root of 9-4)

$\sqrt[3]{3} (5 \sqrt[3]{9} - 4)$

Step 1

Apply the distributive property.

$\sqrt[3]{3} (5 \sqrt[3]{9}) + \sqrt[3]{3} \cdot - 4$

Step 2

Multiply $\sqrt[3]{3} (5 \sqrt[3]{9})$ .

Combine using the product rule for radicals.

$5 \sqrt[3]{3 \cdot 9} + \sqrt[3]{3} \cdot - 4$

Multiply $3$ by $9$ .

$5 \sqrt[3]{27} + \sqrt[3]{3} \cdot - 4$

Step 3

Move $- 4$ to the left of $\sqrt[3]{3}$ .

$5 \sqrt[3]{27} - 4 \cdot \sqrt[3]{3}$

Step 4

Simplify each term.

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

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

Pull terms out from under the radical, assuming real numbers.

$5 \cdot 3 - 4 \cdot \sqrt[3]{3}$

Multiply $5$ by $3$ .

$15 - 4 \sqrt[3]{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$15 - 4 \sqrt[3]{3}$

Decimal Form:

$9.23100171 \dots$