In an opera house, there are 7777 chairs to be placed, but the organiser of the event arranged all the chairs in such a way that there were as many columns as there were rows. So he had to remove minimum 'n' chairs from the total 7777 charis. The minimum value of n is :

Options

A. 121
B. 44
C. 33
D. 25

Answer

To solve the problem of arranging 7777 chairs in an opera house such that the number of rows is equal to the number of columns, we need to find the largest perfect square less than or equal to 7777.

### Step-by-Step Solution:

1. **Understand the Problem**: We need to arrange chairs in a square formation, meaning the number of rows (r) must equal the number of columns (c). Therefore, the total number of chairs can be expressed as \( n^2 \), where \( n \) is the number of rows (or columns).

2. **Find the Largest Perfect Square**: We need to find the largest integer \( n \) such that \( n^2 \leq 7777 \).

3. **Calculate the Square Root**:
\[ n = \lfloor \sqrt{7777} \rfloor \]
First, we calculate \( \sqrt{7777} \):
\[ \sqrt{7777} \approx 88.2 \]
Thus, \( n = 88 \) since we take the floor value.

4. **Calculate the Perfect Square**: Now, we calculate \( n^2 \):
\[ n^2 = 88^2 = 7744 \]

5. **Determine the Number of Chairs to Remove**: To find the minimum number of chairs to remove, we subtract the largest perfect square from the total number of chairs:
\[ n = 7777 - 7744 = 33 \]

### Final Answer:
The minimum value of \( n \) (the number of chairs to be removed) is **33**.

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