Simplify (2 cube root of 12)(3 cube root of 2)

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

Multiply $(2 \sqrt[3]{12}) (3 \sqrt[3]{2})$ .

Multiply $3$ by $2$ .

$6 \sqrt[3]{12} \sqrt[3]{2}$

Combine using the product rule for radicals.

$6 \sqrt[3]{2 \cdot 12}$

Multiply $2$ by $12$ .

$6 \sqrt[3]{24}$

$6 \sqrt[3]{24}$

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

Factor $8$ out of $24$ .

$6 \sqrt[3]{8 (3)}$

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

$6 \sqrt[3]{2^{3} \cdot 3}$

$6 \sqrt[3]{2^{3} \cdot 3}$

Pull terms out from under the radical.

$6 (2 \sqrt[3]{3})$

Multiply $2$ by $6$ .

$12 \sqrt[3]{3}$

The result can be shown in multiple forms.

Exact Form:

$12 \sqrt[3]{3}$

Decimal Form:

$17.30699484 \dots$

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