Question

find the product in simplest radical form.\\(\sqrt3{10} \cdot \sqrt3{4}\\)\
re root symbol (\\(\sqrt{\square}\\)), type
oot\

Explanation:

Step1: Combine radicals (same index)

$$\sqrt[3]{10} \cdot \sqrt[3]{4} = \sqrt[3]{10 \times 4}$$

Step2: Multiply radicands

$$\sqrt[3]{10 \times 4} = \sqrt[3]{40}$$

Step3: Factor radicand for simplification

$$\sqrt[3]{40} = \sqrt[3]{8 \times 5}$$

Step4: Separate perfect cube factor

$$\sqrt[3]{8 \times 5} = \sqrt[3]{8} \cdot \sqrt[3]{5}$$

Step5: Simplify perfect cube root

$$\sqrt[3]{8} \cdot \sqrt[3]{5} = 2\sqrt[3]{5}$$

Answer:

$2\sqrt[3]{5}$