Out of `745` students, maximum are to be arranged in the school field for a P.T. display, such that the number of rows is equal to the number of columns. Find the number of rows if `16` students were left out after the arrangement.

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Determine the number of students that can be arranged
We start with the total number of students, which is 745. Since 16 students are left out, we need to subtract these from the total.

\[ \text{Number of students that can be arranged} = 745 - 16 = 729 \]

### Step 2: Set up the equation for rows and columns
We need to arrange the students in such a way that the number of rows is equal to the number of columns. If we denote the number of rows (and columns) as \( a \), then the total number of students that can be arranged is given by:

\[ a \times a = a^2 \]

This means:

\[ a^2 = 729 \]

### Step 3: Solve for \( a \)
To find the value of \( a \), we need to take the square root of both sides of the equation:

\[ a = \sqrt{729} \]

### Step 4: Calculate the square root
Now we calculate the square root of 729.

\[ \sqrt{729} = 27 \]

### Conclusion
Thus, the number of rows (and columns) that can be arranged is:

\[ \text{Number of rows} = 27 \]