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

Difficulty: Easy

Correct Answer: 47

Explanation:


Introduction / Context:
This item checks rapid recognition of perfect squares. Among the given numbers, three are squares of integers, while one is not. Your task is to pick the non-square at a glance using common square values.



Given Data / Assumptions:

  • 4 = 2^2.
  • 64 = 8^2.
  • 225 = 15^2.
  • 47 is not an integer square (sqrt(47)≈6.855...).


Concept / Approach:
Recall squares up to at least 20^2 and match. Alternatively, factorize: a perfect square’s prime exponents are all even.



Step-by-Step Solution:

Confirm 4, 64, 225 are squares.Evaluate 47: prime and not a square.Therefore, 47 is the odd one out.


Verification / Alternative check:
Take square roots: only 4, 64, 225 yield integer roots; 47 does not.



Why Other Options Are Wrong:

They are perfect squares and thus do not meet the “non-square” criterion.


Common Pitfalls:
Confusing 225 with 250 or 256 (16^2). Remember 15^2=225.



Final Answer:
47

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