Classification – Perfect squares vs non-square: three numbers are perfect squares; one is not. Which is the odd one out? Options: 210, 529, 289, 196.

Introduction / Context:One common numeric contrast is square versus non-square. Recognizing classic square values isolates the outlier quickly.

Given Data / Assumptions:

• 529 = 23^2.
• 289 = 17^2.
• 196 = 14^2.
• 210 is not a perfect square; it lies between 14^2=196 and 15^2=225.

Concept / Approach:Confirm square status via known squares or factorization.

Step-by-Step Solution:Mark 529, 289, 196 as squares.Mark 210 as non-square.Select 210 as the odd one out.

Verification / Alternative check:Prime factorization of 210 = 2 * 3 * 5 * 7 includes no repeated prime factors, so it cannot be a square.

Why Other Options Are Wrong:529/289/196: Each is exactly n^2 for integer n.

Common Pitfalls:Mistaking 225 (15^2) for 210; the latter is not square.

Final Answer:210