A General of army wants to arrange 36562 soldiers in equal number of rows and columns .After the arrangement ,he found that some soldiers were left . How many soldiers were left ?

Options

A. 36
B. 65
C. 81
D. 97

Answer

To find out how many soldiers were left after arranging 36562 soldiers in equal rows and columns, we need to determine the largest perfect square less than or equal to 36562. The number of soldiers left will be the difference between 36562 and that perfect square.

### Step-by-Step Solution:

1. **Identify the Number of Soldiers**:
The total number of soldiers is 36562.

2. **Find the Square Root**:
We need to find the largest integer \( n \) such that \( n^2 \leq 36562 \).
- Calculate \( \sqrt{36562} \).
- \( \sqrt{36562} \approx 191.1 \).
- The largest integer \( n \) is 191.

3. **Calculate the Perfect Square**:
Now, we calculate \( n^2 \):
- \( 191^2 = 36481 \).

4. **Calculate the Soldiers Left**:
To find how many soldiers are left after arranging them in rows and columns:
- Subtract the perfect square from the total soldiers:
- \( 36562 - 36481 = 81 \).

5. **Final Answer**:
Therefore, the number of soldiers left is **81**.

### Summary:
The General of the army will have **81 soldiers left** after arranging the other soldiers in equal rows and columns.