Simplify cube root of 3( cube root of 4+ cube root of 32)

$\sqrt[3]{3} (\sqrt[3]{4} + \sqrt[3]{32})$

Simplify each term.

Rewrite $32$ as $2^{3} \cdot 4$ .

Factor $8$ out of $32$ .

$\sqrt[3]{3} (\sqrt[3]{4} + \sqrt[3]{8 (4)})$

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

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

Pull terms out from under the radical.

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

Add $\sqrt[3]{4}$ and $2 \sqrt[3]{4}$ .

$\sqrt[3]{3} (3 \sqrt[3]{4})$

Multiply $\sqrt[3]{3} (3 \sqrt[3]{4})$ .

Combine using the product rule for radicals.

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

Multiply $3$ by $4$ .

$3 \sqrt[3]{12}$

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt[3]{12}$

Decimal Form:

$6.86828545 \dots$