Classification (numbers – perfect squares): Three numbers are perfect squares; one is not a perfect square. Identify the odd number.

Difficulty: Easy

Correct Answer: 18

Explanation:


Introduction / Context:
Number classification often tests recognition of perfect squares. Among the given numbers, three are perfect squares of integers; one is not. The task is to select the non-square number quickly and confidently.



Given Data / Assumptions:

  • Known squares: 3^2=9, 4^2=16, 5^2=25.
  • 18 is not an integer square (sqrt(18)≈4.2426...).


Concept / Approach:
Check each number against a memorized square table up to at least 20^2. Alternatively, factorize: a perfect square has even exponents in prime factorization.



Step-by-Step Solution:

9 → perfect square (3^2).16 → perfect square (4^2).25 → perfect square (5^2).18 → factorize 18=2*3^2 (exponent of 2 is odd) → not a square.


Verification / Alternative check:
Take square roots: only 9,16,25 yield integers; 18 does not.



Why Other Options Are Wrong:

They are perfect squares and therefore do not satisfy the “non-square” criterion.


Common Pitfalls:
Misremembering squares around 20–30. Sticking to a simple checklist (9,16,25) prevents errors.



Final Answer:
18

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