Mr. Tyagi is a yoga instructor. He wants his 600 students to sit in such a manner that the number of rows is equal to number of columns. How many students will be left out in this arrangement?

Options

A. 14
B. 24
C. 50
D. None

Answer

To solve the problem, we need to arrange 600 students in a way that the number of rows is equal to the number of columns. This means we are looking for a perfect square arrangement.

### Step-by-Step Solution:

1. **Identify the Total Number of Students**:
The total number of students is given as 600.

2. **Determine the Largest Perfect Square Less Than 600**:
We need to find the largest integer \( n \) such that \( n^2 \) is less than or equal to 600. This will give us the maximum number of students that can be arranged in a square formation.

3. **Calculate the Square Root of 600**:
We can find the square root of 600 to determine the largest integer \( n \):
\[ \sqrt{600} \approx 24.49 \]
Since \( n \) must be a whole number, we take the integer part, which is 24.

4. **Calculate the Perfect Square**:
Now, we calculate \( n^2 \):
\[ 24^2 = 576 \]
This means that 576 students can be arranged in a square formation of 24 rows and 24 columns.

5. **Calculate the Number of Students Left Out**:
To find out how many students will be left out, we subtract the number of students that can be arranged in the square from the total number of students:
\[ \text{Students left out} = 600 - 576 = 24 \]

6. **Final Answer**:
Therefore, the number of students that will be left out in this arrangement is **24**.