In the following question, select the odd number from the alternatives given below. Check whether each number has a special property (such as being a perfect square). Identify the number that does NOT share that property with the others. (A) 361 (B) 441 (C) 784 (D) 876 (E) 1024

Introduction / Context:This odd-one-out problem checks number properties, most commonly perfect squares. A perfect square is an integer that can be expressed as n*n for some whole number n. The odd number is the one that cannot be written as a square, while the others can.

Given Data / Assumptions:

• A number is a perfect square if it equals n*n for some integer n.
• We test each option by recalling common squares or checking nearby squares.
• If several numbers are exact squares and one is not, that one is the odd choice.

Concept / Approach:Recognize perfect squares by memory (like 19^2, 21^2, 28^2) or by checking whether the number lies exactly on a square boundary. Non-squares will fall between two consecutive squares.

Step-by-Step Solution:

Verification / Alternative check:Another quick check is to compute the integer square root estimate. Since 29^2=841 and 30^2=900, any number between them is not a square. Because 876 lies strictly between these, it cannot be expressed as n*n for an integer n. Hence it is the odd one out.

Why Other Options Are Wrong:

Common Pitfalls:A common mistake is assuming any even number is not a square or any number ending in 1 is a square. Another mistake is checking only the last digit. Always confirm by matching to an exact integer multiplication (n*n) or bounding between consecutive squares.

Final Answer:876