for helping poor people, a club is collecting funds. each member contributes as many rupees as there are members. of total collection is rupees 38416 , find the number of members in club .

Let's denote the number of members in the club as \( n \). According to the problem, each member contributes \( n \) rupees, and since there are \( n \) members, the total contribution is given by \( n \times n = n^2 \).

We are told that the total collection is 38416 rupees. Therefore, we have the equation:

\[
n^2 = 38416
\]

To find the number of members, \( n \), we take the square root of both sides:

\[
n = \sqrt{38416}
\]

Calculating the square root of 38416:

\[
n = 196
\]

So, the number of members in the club is **196**.

Would you like further details or have any questions?

Here are five related questions:
1. How would the total collection change if each member contributed twice as many rupees?
2. What would be the total collection if there were 10 fewer members?
3. How do you calculate the square root of a large number manually?
4. If the number of members doubled, what would be the new total collection?
5. Can you derive a general formula for the total collection if each member contributes a different fixed amount?

**Tip:** When working with large numbers, estimating square roots can be simplified by recognizing perfect squares close to the number.

Explore how to determine the number of club members and their contributions in a fundraising scenario where each member contributes an amount equal to the total number of members. Solve the problem step-by-step with a detailed explanation and find out how to calculate square roots effectively. Suitable for students in Grades 7-9.

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