Find the Product cube root of 24* cube root of 45

$\sqrt[3]{24} \cdot \sqrt[3]{45}$

Step 1

Combine using the product rule for radicals.

$\sqrt[3]{24 \cdot 45}$

Step 2

Multiply $24$ by $45$ .

$\sqrt[3]{1080}$

Step 3

Rewrite $1080$ as $6^{3} \cdot 5$ .

Factor $216$ out of $1080$ .

$\sqrt[3]{216 (5)}$

Rewrite $216$ as $6^{3}$ .

$\sqrt[3]{6^{3} \cdot 5}$

$\sqrt[3]{6^{3} \cdot 5}$

Step 4

Pull terms out from under the radical.

$6 \sqrt[3]{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt[3]{5}$

Decimal Form:

$10.25985568 \dots$

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