Classification – Odd one out (perfect squares) Three of the following numbers are perfect squares, whereas one number is not a perfect square. Identify the non-square and mark it as the odd one out.

Introduction / Context:Recognizing perfect squares rapidly is a core skill for classification problems. Test-makers often choose square numbers that are near famous benchmarks or that arise from simple integer pairs, making them straightforward for well-prepared candidates to spot. The task here is to separate the single non-square from three genuine squares by confirming exact equality to some k^2 rather than relying on guesswork or approximate magnitudes.

Given Data / Assumptions:

• Options: 64, 169, 484, 315
• We must find the value that is not equal to any integer square.

Concept / Approach:Recall common squares: 8^2 = 64, 13^2 = 169, 22^2 = 484. For any candidate, compare against a nearby square to see whether it equals k^2 for some integer k. If it does not match exactly, it is not a perfect square. Estimating the square root and checking for an integer result is another reliable route (e.g., sqrt(315) is between 17 and 18 but not an integer).

Step-by-Step Solution:64 = 8^2 → perfect square.169 = 13^2 → perfect square.484 = 22^2 → perfect square.315: 17^2 = 289 and 18^2 = 324; 315 lies strictly between them → not a perfect square.

Verification / Alternative check:Confirm with square-root estimation: sqrt(315) is approximately 17.75. Since it is not an integer, 315 cannot be an exact square. In contrast, 64, 169, and 484 match exact k^2 values, removing doubt about their status as perfect squares.

Why Other Options Are Wrong:

• 64: Exactly equals 8^2.
• 169: Exactly equals 13^2.
• 484: Exactly equals 22^2.
• None of these: There is a single non-square (315), so this distractor is not correct.

Common Pitfalls:Assuming that being near a square (such as 315 near 324) is sufficient. Only exact equality to k^2 defines a perfect square; “close” does not count.

Final Answer:315