Class donation equals a perfect square: Students of Class XI jointly donate ₹ 4356, and each student contributes an amount equal to the number of students. Find the class strength.

Introduction / Context:
This is another perfect square total problem. If each of n students donates n rupees, the total becomes n^2 rupees. Recognizing perfect squares quickly is a useful arithmetic skill.

Given Data / Assumptions:
Total donation = ₹ 4356, each student pays = number of students.

Concept / Approach:
Total = n × n = n^2. Hence, n = √4356. Compute the exact square root.

Step-by-Step Solution:
66^2 = (60 + 6)^2 = 3600 + 720 + 36 = 4356.Therefore, n = 66 students.

Verification / Alternative check:
Multiplying 66 × 66 confirms 4356 precisely.

Why Other Options Are Wrong:
60, 64, 65, 70 do not square to 4356; their squares differ from the required total.

Common Pitfalls:
Mis-squaring nearby numbers (e.g., mixing up 64^2 = 4096 or 70^2 = 4900) or assuming the number must be round like 60 or 70.

Final Answer:
66