Problem 72

Question

Simplify the radical expressions if possible. $$\sqrt[3]{12} \cdot \sqrt[3]{4}$$

Step-by-Step Solution

Verified
Answer
\( \sqrt[3]{48} \)
1Step 1: Multiply the radicands
Combine the two cube root expressions under one cube root by multiplying the radicands 12 and 4. This gives us \( \sqrt[3]{12 \cdot 4} \).
2Step 2: Simply the multiplication
Next, multiply the radicands together. This leaves us with \( \sqrt[3]{48} \).
3Step 3: Simplify the cube root
Simplify the cube root of 48 if possible. However, 48 doesn't have a perfect cube factor and hence can't be simplified further. Therefore, the final simplified form of the expression is \( \sqrt[3]{48} \).