Simplify cube root of 2( cube root of 4+ cube root of 12)

$\sqrt[3]{2} (\sqrt[3]{4} + \sqrt[3]{12})$

Step 1

Simplify terms.

Apply the distributive property.

$\sqrt[3]{2} \sqrt[3]{4} + \sqrt[3]{2} \sqrt[3]{12}$

Combine using the product rule for radicals.

$\sqrt[3]{2 \cdot 4} + \sqrt[3]{2} \sqrt[3]{12}$

Combine using the product rule for radicals.

$\sqrt[3]{2 \cdot 4} + \sqrt[3]{2 \cdot 12}$

Step 2

Simplify each term.

Multiply $2$ by $4$ .

$\sqrt[3]{8} + \sqrt[3]{2 \cdot 12}$

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

$\sqrt[3]{2^{3}} + \sqrt[3]{2 \cdot 12}$

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

$2 + \sqrt[3]{2 \cdot 12}$

Multiply $2$ by $12$ .

$2 + \sqrt[3]{24}$

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

Factor $8$ out of $24$ .

$2 + \sqrt[3]{8 (3)}$

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

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

Pull terms out from under the radical.

$2 + 2 \sqrt[3]{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 + 2 \sqrt[3]{3}$

Decimal Form:

$4.88449914 \dots$