Among the following four numbers, three are perfect squares of positive integers and one number is not a perfect square. By using your knowledge of square numbers, select the number that is the odd one out.

Introduction / Context:
This question tests your familiarity with perfect squares and your ability to quickly recognize them. In many aptitude exams, you are given a group of numbers where all but one obey a specific property, such as being perfect squares, perfect cubes, or prime numbers. Your task here is to identify which of the four given numbers is not a perfect square. Recognizing square numbers is a useful mental skill in quantitative aptitude, number system questions, and simplification problems.

Given Data / Assumptions:
- The numbers given are 961, 443, 361, and 289.
- A perfect square is a number that can be written as n^2 for some positive integer n.
- We assume standard arithmetic with no tricks or special bases.

Concept / Approach:
To solve this, recall commonly used square numbers. For example, 17^2 = 289, 19^2 = 361, and 31^2 = 961. Any number that does not match a known integer square is not a perfect square. It is efficient to remember square values at least up to 35^2 for competitive exams. When in doubt, you can try to approximate the square root and see whether it is an integer.

Step-by-Step Solution:
Step 1: Check 289. Since 17 * 17 = 289, this number is a perfect square of 17.Step 2: Check 361. We know that 19 * 19 = 361, so 361 is a perfect square of 19.Step 3: Check 961. Observe that 30^2 = 900 and 31^2 = 961, so 961 is a perfect square of 31.Step 4: Check 443. Nearby squares are 21^2 = 441 and 22^2 = 484. Since 443 is between 441 and 484 and not equal to either, it is not a perfect square.Step 5: Conclude that 443 is the only number among the four that is not a perfect square.

Verification / Alternative check:
To verify, we can approximate the square root of 443. It lies between 21 and 22 because 21^2 = 441 and 22^2 = 484. Since there is no integer n such that n^2 = 443, the number cannot be a perfect square. The other three numbers correspond exactly to integer squares that are often memorised for exam practice.

Why Other Options Are Wrong:
961 is wrong as the odd one because it clearly equals 31^2, so it satisfies the perfect square property. Similarly, 361 equals 19^2 and 289 equals 17^2, so both are perfect squares. Since these three meet the same condition, they are part of the majority group and cannot be the odd one out.

Common Pitfalls:
Students sometimes confuse 289 with 17 * 19 or mix up nearby square values. Another mistake is to stop after checking only one or two numbers and guessing the answer without verifying all options. Some candidates also attempt long division style square root calculations, which is slow under exam constraints. Instead, memorizing square values up to at least 35^2 and using quick comparison with nearby squares is more efficient.

Final Answer:
The odd number is 443, because it is not a perfect square, while the other three numbers are perfect squares of 17, 19, and 31 respectively.