Find the odd number from the alternatives given below. Three numbers are perfect squares, while one is not a perfect square. Identify the odd one out. (A) 16 (B) 4 (C) 2 (D) 36 (E) 81
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A16
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B4
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C2
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D36
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E81
Answer
Correct Answer: 2
Explanation
Introduction / Context:This odd-one-out question checks the concept of perfect squares. A perfect square is a number that can be written as n*n for an integer n. The odd number will be the one that cannot be expressed in that form, while the others can.
Given Data / Assumptions:
- Perfect square means: number = n*n for some integer n.
- We verify by matching the number to known squares (2^2, 3^2, 4^2, etc.).
- If one option is not a square while others are, it is the odd one out.
Concept / Approach:Identify which numbers are squares of integers. If 4 out of 5 are perfect squares and one is not, the non-square is the odd option.
Step-by-Step Solution:
16 = 4*4, so 16 is a perfect square. 4 = 2*2, so 4 is a perfect square. 36 = 6*6, so 36 is a perfect square. 81 = 9*9, so 81 is a perfect square. 2: there is no integer n such that n*n = 2, so 2 is not a perfect square.Verification / Alternative check:You can also check by bounding: 1^2 = 1 and 2^2 = 4. Since 2 lies between 1 and 4 and is not equal to either, it cannot be a perfect square. This confirms that 2 is the odd number in the group.
Why Other Options Are Wrong:
16: equals 4^2, so it matches the perfect-square property. 4: equals 2^2, so it matches the perfect-square property. 36: equals 6^2, so it matches the perfect-square property. 81: equals 9^2, so it matches the perfect-square property.Common Pitfalls:Some students confuse 'even numbers' with 'perfect squares' and assume all even numbers are squares, which is false. Another pitfall is checking only the last digit: while squares often end in 0,1,4,5,6,9, that alone is not sufficient to prove squareness. Always confirm with an exact integer multiplication or bounding between consecutive squares.
Final Answer:2