Choose the odd number: In 25, 64, 189, and 441, three are perfect squares (n^2) and one is not. Identify the non-square.

Introduction / Context:Perfect-square detection is a standard classification skill.

Given Data / Assumptions:

• Numbers: 25 = 5^2, 64 = 8^2, 441 = 21^2, 189 = ?
• We test whether 189 equals n^2 for an integer n.

Concept / Approach:Use known squares or check between consecutive squares.

Step-by-Step Solution:

Verification / Alternative check:Prime factorization 189 = 3^3 * 7 has exponents not all even; hence not a square.

Why Other Options Are Wrong:25, 64, and 441 are exact squares.

Common Pitfalls:Assuming “near a square” implies squareness; exact equality is required.

Final Answer:189 is the non-square.