Question

simplify the radical expression. (sqrt3{4} cdot sqrt3{6}) (sqrt3{4} cdot sqrt3{6} = square)

Explanation:

Step1: Combine cube roots

$\sqrt[3]{4} \cdot \sqrt[3]{6} = \sqrt[3]{4 \cdot 6}$

Step2: Multiply inside the root

$\sqrt[3]{4 \cdot 6} = \sqrt[3]{24}$

Step3: Factor 24 for simplification

$\sqrt[3]{24} = \sqrt[3]{8 \cdot 3}$

Step4: Separate perfect cube factor

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

Step5: Simplify perfect cube root

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

Answer:

$2\sqrt[3]{3}$