Identify the odd number: Three are squares of prime numbers (13^2, 17^2, 19^2 after repair), while one is a square of a composite number (15^2). Choose the square of the composite.

Introduction / Context:
The original options contained a duplicate “225”. Under the Recovery-First policy, we minimally repair by treating the fourth entry as the next consistent prime square, 361 (which is 19^2). Now the set contrasts prime squares with one composite-base square.

Given Data / Assumptions:

• 169 = 13^2 (prime base).
• 289 = 17^2 (prime base).
• 361 = 19^2 (prime base).
• 225 = 15^2 (composite base; 15 = 3 * 5).

Concept / Approach:
Classify by the nature of the base n whose square forms n^2: prime vs composite.

Step-by-Step Solution:

Verification / Alternative check:
Factor 225 = 3^2 * 5^2; its base (15) is composite.

Why Other Options Are Wrong:
169, 289, and 361 are squares of primes, sharing the majority property.

Common Pitfalls:
Overlooking the duplicate and ending with two “correct” entries; minimal repair ensures a single unambiguous answer.

Final Answer:
225 is the square of a composite and is the odd number.