The equation given is $x^2 = 228$, where $x$ represents the length of the diagonal of the square in centimeters. To find the value of $x$, we need to take the square root of both sides of the equation:

$x = \sqrt{228}$

Calculating the square root:

$x \approx \sqrt{228} \approx 15.1 \, \text{cm}$

So, the length of the diagonal of the square is approximately $15.1$ centimeters.

Would you like more details on this calculation or have any other questions?

Here are 8 related questions for further exploration:

1. What is the area of a square if the length of its diagonal is $15.1$ cm?
2. How do you derive the diagonal of a square from its side length?
3. If the side length of the square was known, how would you calculate its diagonal?
4. What is the relationship between the diagonal and the perimeter of a