Problem 71 - College Algebra

Question

Simplify the radical expressions if possible. $$\sqrt[3]{9} \cdot \sqrt[3]{6}$$

Step-by-Step Solution

Answer

The answer is \( \sqrt[3]{54} \).

Step 1: Understanding the problem

The problem asks to simplify \( \sqrt[3]{9} \cdot \sqrt[3]{6} \). This means we need to multiply the numbers inside the cube roots, which is 9 and 6.

Step 2: Perform the multiplication

Multiply the numbers inside the cube roots together. \( \sqrt[3]{9} \cdot \sqrt[3]{6} \) equals \( \sqrt[3]{9 \cdot 6} \) which is equal to \( \sqrt[3]{54} \).

Step 3: Look for simplification

In the final step, we look for any possible simplification. However, 54 cannot be simplified if it remains under cube root because it is not a cube of any integer. So, our final result is \( \sqrt[3]{54} \).