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The problem is asking how many soldiers need to be removed from or added to 56,728 soldiers so that the total number of soldiers can form a perfect square. 

To solve this, we will find the nearest perfect squares to 56,728.

### Steps:
1. Calculate the square root of 56,728.
2. Round the square root to the nearest whole numbers to find the closest perfect squares.
3. Compare the total soldiers with these squares and calculate how many need to be removed or added.

Let's calculate this.The square root of 56,728 is approximately 238.18. The nearest perfect squares are:

- \( 238^2 = 56,644 \) (lower square)
- \( 239^2 = 57,121 \) (upper square)

Thus, to arrange the soldiers in a square:

- **Remove** at least 84 soldiers to get 56,644 soldiers (a perfect square).
- **Add** at least 393 soldiers to get 57,121 soldiers (a perfect square).

Would you like further details or have any questions?

Here are 5 related questions:
1. How do we calculate perfect squares and square roots manually?
2. Can the problem be extended to different numbers of soldiers?
3. What is the significance of arranging in a perfect square in real-world scenarios?
4. How can we determine the smallest number of additions or subtractions for other geometric shapes (e.g., cubes)?
5. How does rounding affect calculations in this type of problem?

**Tip:** Perfect squares are numbers like \(1^2\), \(2^2\), \(3^2\), and so on, which are used to arrange objects in a complete square formation.

If at least how many soldiers are removed from 56,728 soldiers or at least how many more soldiers are added to them, the army can be arranged in a square?

Learn how to arrange 56,728 soldiers into a perfect square by either removing 84 soldiers or adding 393. This problem involves calculating square roots, rounding, and understanding perfect squares. Ideal for students in Grades 8-10.

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