4726 soldiers are divided in two groups to make a solid square. It is found that some extra soldiers are in the 2nd group. If 32 rows in the first group then find the least extra soldiers in 2nd group.

Options

A. 32
B. 4136
C. 100
D. 102

Answer

To solve the problem, we need to find out how many soldiers are in the first group, how many are left for the second group, and then determine the least extra soldiers in the second group.

### Step-by-Step Solution:

1. **Identify the total number of soldiers:**
The total number of soldiers is given as 4726.

2. **Determine the number of soldiers in the first group:**
The problem states that there are 32 rows in the first group. Since we want to form a solid square, we can assume that each row has the same number of soldiers. Therefore, we need to find out how many soldiers are in each row.

\[ \text{Number of soldiers in each row} = 32 \]

The total number of soldiers in the first group can be calculated as:
\[ \text{Total soldiers in the first group} = 32 \times 32 = 1024 \]

3. **Calculate the number of soldiers left for the second group:**
Now, we subtract the number of soldiers in the first group from the total number of soldiers to find out how many are left for the second group.

\[ \text{Soldiers in the second group} = 4726 - 1024 = 3702 \]

4. **Determine the least extra soldiers in the second group:**
To form a solid square, the number of soldiers in the second group should also be a perfect square. We need to find the largest perfect square less than or equal to 3702.

The largest perfect square less than 3702 is:
\[ 60^2 = 3600 \]

Now, we can find the least extra soldiers in the second group by subtracting this perfect square from the total soldiers in the second group.

\[ \text{Least extra soldiers} = 3702 - 3600 = 102 \]

### Final Answer:
The least extra soldiers in the second group is **102**.