Choose the odd number: Three numbers are perfect squares; one is not. Identify the number that is NOT a perfect square.

Difficulty: Easy

Correct Answer: 210

Explanation:


Introduction / Context:
Perfect squares are integers of the form n^2. This classification task asks you to spot the one number that is not a perfect square among otherwise familiar squares.


Given Data / Assumptions:

  • Options: 144, 169, 196, 210.
  • Recall: 12^2 = 144, 13^2 = 169, 14^2 = 196.


Concept / Approach:
Check each option against nearby square values, or determine whether its integer square root exists. A non-square will not match any n^2 exactly.


Step-by-Step Solution:

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


Verification / Alternative check:
Take integer square roots: sqrt(144) = 12, sqrt(169) = 13, sqrt(196) = 14 are integers. sqrt(210) is not an integer, confirming non-square status.


Why Other Options Are Wrong:
They are exact perfect squares and hence do not answer the “odd number” request.


Common Pitfalls:
Assuming that being near a square (e.g., 210 near 196 and 225) is enough. Only exact equality to n^2 counts.


Final Answer:
210 is not a perfect square.

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