Simplify cube root of 2( cube root of 135-4 cube root of 5)

$\sqrt[3]{2} (\sqrt[3]{135} - 4 \sqrt[3]{5})$

Simplify each term.

Rewrite $135$ as $3^{3} \cdot 5$ .

Factor $27$ out of $135$ .

$\sqrt[3]{2} (\sqrt[3]{27 (5)} - 4 \sqrt[3]{5})$

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

$\sqrt[3]{2} (\sqrt[3]{3^{3} \cdot 5} - 4 \sqrt[3]{5})$

Pull terms out from under the radical.

$\sqrt[3]{2} (3 \sqrt[3]{5} - 4 \sqrt[3]{5})$

Subtract $4 \sqrt[3]{5}$ from $3 \sqrt[3]{5}$ .

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

Multiply $\sqrt[3]{2} (- \sqrt[3]{5})$ .

Combine using the product rule for radicals.

$- \sqrt[3]{2 \cdot 5}$

Multiply $2$ by $5$ .

$- \sqrt[3]{10}$

The result can be shown in multiple forms.

Exact Form:

$- \sqrt[3]{10}$

Decimal Form:

$- 2.15443469 \dots$