Classification – Odd one out (three perfect squares vs one non-square) In the set below, three numbers are perfect squares, whereas one is not a perfect square. Identify the non-square as the odd one out.

Introduction / Context:
A classic classification pattern contrasts perfect squares with a lone non-square. Recognizing 4^2 = 16, 5^2 = 25, and 7^2 = 49 quickly reveals the outlier.

Given Data / Assumptions:

• Set: 16, 25, 35, 49
• We must find the single non-square.

Concept / Approach:
Match candidates to familiar squares. If a value does not equal k^2 for any integer k, it is not a perfect square.

Step-by-Step Solution:
16 = 4^2 → square.25 = 5^2 → square.49 = 7^2 → square.35 is between 5^2 = 25 and 6^2 = 36 → not a square.

Verification / Alternative check:
sqrt(35) ≈ 5.916… is non-integral, confirming 35 is not a perfect square.

Why Other Options Are Wrong:

• 16: Exact square.
• 25: Exact square.
• 49: Exact square.
• None of these: There is clearly one non-square (35).

Common Pitfalls:
Assuming “odd = non-square.” Many odd numbers are squares (e.g., 25, 49). Always verify with known square facts.

Final Answer:
35