Choose the odd number: Three of the following are perfect squares (n^2), while one is not. Identify the non-square.

Difficulty: Easy

Correct Answer: 18

Explanation:


Introduction / Context:
Recognizing perfect squares is a foundational skill for quantitative aptitude. In this classification task, three options are exact squares of integers; one is not. Spot the non-square.


Given Data / Assumptions:

  • Options: 25, 9, 16, 18.
  • Recall: 5^2 = 25, 3^2 = 9, 4^2 = 16.


Concept / Approach:
Compare each number to known square values or compute integer square roots. A non-square will not match n^2 for any integer n.


Step-by-Step Solution:

25 = 5^2 → perfect square.9 = 3^2 → perfect square.16 = 4^2 → perfect square.18 lies between 4^2 = 16 and 5^2 = 25 and thus is not a perfect square.


Verification / Alternative check:
Take integer square roots: sqrt(25) = 5, sqrt(9) = 3, sqrt(16) = 4 are integers; sqrt(18) is irrational, confirming non-square status.


Why Other Options Are Wrong:
They are exact perfect squares and therefore not the odd item.


Common Pitfalls:
Assuming that being near a perfect square makes a number a square; exact equality to n^2 is required.


Final Answer:
18 is the only non-square.

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