The square on the diagonal of a cube has an area of `192 cm ^(2) `Calculate :
the side of the cube.

Answer

To solve the problem, we need to find the side length of a cube given that the area of the square on the diagonal of the cube is \(192 \, \text{cm}^2\).

### Step-by-step Solution:

1. **Understand the relationship between the side of the cube and the diagonal:**
- Let the side length of the cube be \(A\).
- The formula for the length of the diagonal \(d\) of a cube is given by:
\[ d = A\sqrt{3} \]

2. **Determine the area of the square on the diagonal:**
- The area of the square formed on the diagonal is given as \(192 \, \text{cm}^2\).
- The area of a square is calculated as the square of its side length. Therefore, if the side of the square is equal to the diagonal \(d\), we have:
\[ \text{Area} = d^2 = (A\sqrt{3})^2 \]

3. **Set up the equation:**
- From the area given, we can write:
\[ (A\sqrt{3})^2 = 192 \]
- Simplifying this gives:
\[ 3A^2 = 192 \]

4. **Solve for \(A^2\):**
- To isolate \(A^2\), divide both sides by \(3\):
\[ A^2 = \frac{192}{3} = 64 \]

5. **Find \(A\):**
- To find \(A\), take the square root of both sides:
\[ A = \sqrt{64} = 8 \]

6. **Conclusion:**
- The side length of the cube is \(8 \, \text{cm}\).

### Final Answer:
The side of the cube is \(8 \, \text{cm}\).