Classification – Odd one out (three perfect squares vs one non-square) Among the following numbers, three are perfect squares and one is not. Identify the non-square and mark it as the odd one out.

Introduction / Context:This item checks rapid recognition of standard squares: 12^2 = 144, 13^2 = 169, 14^2 = 196. Spotting the outsider reinforces square benchmarks crucial for speed in classification tasks.

Given Data / Assumptions:

• Candidates: 144, 169, 196, 210
• Goal: find the single non-square.

Concept / Approach:Confirm equality to k^2 for small integers. If a value lies strictly between consecutive squares, it cannot be a perfect square.

Step-by-Step Solution:144 = 12^2 → square.169 = 13^2 → square.196 = 14^2 → square.210 is between 14^2 = 196 and 15^2 = 225 → not a perfect square.

Verification / Alternative check:Square-root estimation: sqrt(210) ≈ 14.49, not an integer, confirming non-square status.

Why Other Options Are Wrong:

• 144: Exact square.
• 169: Exact square.
• 196: Exact square.
• None of these: 210 is uniquely non-square.

Common Pitfalls:Mistaking “close to a square” as sufficient. Only exact equality qualifies.

Final Answer:210