Consider a cube with a volume of 64 cm^(3). What can be concluded about the cube? Select the two that apply.

To analyze the cube with a volume of 64 cm³, we can recall that the volume \( V \) of a cube is calculated using the formula \( V = s^3 \), where \( s \) is the side length.

1. **Taking the cube root of its volume will determine its side length.** - This statement is true. To find the side length \( s \), you can take the cube root of the volume: \( s = \sqrt[3]{V} \).

2. **The side length is 8 cm.** - This statement is true. If you calculate the cube root of the volume \( \sqrt[3]{64} = 4 \), you will find that the side length is actually 4 cm. Hence this statement is incorrect.

3. **The side length is 4 cm.** - This statement is true. As calculated, the cube root of 64 is 4, which is the side length.

4. **The expression \( s^{2} \), where \( s \) represents the side length was used to solve this problem.** - This statement is false. The expression that relates to finding the volume is \( s^3 \), not \( s^2 \).

Based on the analysis, the two correct conclusions are:

A. Taking the cube root of its volume will determine its side length.
B. The side length is 4 cm.