Choose the odd number: Three of the following are perfect squares (n^2), while one is not. Identify the non-square.
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A25
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B9
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C16
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D18
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ENone of these
Answer
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.