Answer :
Answer:To find out how many rows there are in the auditorium, we need to determine the number of rows and the number of students per row. Given that the number of students in a row is equal to the number of rows, the total number of students can be expressed as:
\[ n \times n = 4096 \]
where \( n \) is the number of rows and also the number of students per row. This can be simplified to:
\[ n^2 = 4096 \]
To find \( n \), we take the square root of both sides of the equation:
\[ n = \sqrt{4096} \]
Next, we calculate the square root of 4096:
\[ \sqrt{4096} = 64 \]
Thus, the number of rows in the auditorium is:
\[ n = 64 \]
### Answer:
There are 64 rows in the auditorium.
Step-by-step explanation:Sure, let's go through the step-by-step process to determine the number of rows in the auditorium.
### Given:
- Total number of students = 4096
- The number of students in each row is equal to the number of rows.
### Step-by-Step Explanation:
1. **Express the total number of students in terms of rows and students per row:**
Let's denote the number of rows (and the number of students per row) as \( n \).
The total number of students can be expressed as:
\[
n \times n = 4096
\]
2. **Simplify the equation:**
The equation \( n \times n = 4096 \) can be rewritten as:
\[
n^2 = 4096
\]
3. **Solve for \( n \):**
To find \( n \), we need to take the square root of both sides of the equation:
\[
n = \sqrt{4096}
\]
4. **Calculate the square root of 4096:**
\[
\sqrt{4096} = 64
\]
5. **Conclusion:**
Since \( n = 64 \), the number of rows in the auditorium is 64. This means there are 64 rows, and each row has 64 students.
### Final Answer:
There are 64 rows in the auditorium.
