In the following question, select the odd word/letters/number/number pair from the given alternatives: 794, 576, 668 and 992. Three of these numbers are not perfect squares, while one number is a perfect square. Based on this property, which number is the odd one out?

Introduction / Context:
This question is a numerical odd one out problem, where you must select the number that differs from the others based on an important mathematical property. Here, three numbers are non-perfect squares, while one is a perfect square. Recognising perfect squares quickly is very useful in quantitative aptitude and number system questions.

Given Data / Assumptions:

• Numbers: 794, 576, 668, 992.
• We will check whether each number can be expressed as n^2 for some integer n.
• A number that is exactly the square of an integer is called a perfect square.
• Three numbers will not be perfect squares; one will be, and that will be the odd one out.

Concept / Approach:
The idea is to factorise or recall squares around the approximate square roots:

• Find the nearest integer square roots.
• Check whether squaring those integers gives the exact number.

If the number equals some integer squared, it is a perfect square; otherwise, it is not. We then identify which number stands out due to this property.

Step-by-Step Solution:
Step 1: Check 576. We know 24 * 24 = 576. So 576 = 24^2, which is a perfect square. Step 2: Check 794. Find nearby squares: 28^2 = 784, 29^2 = 841. 794 lies between 784 and 841 and is not equal to either, so 794 is not a perfect square. Step 3: Check 668. Nearby squares: 25^2 = 625, 26^2 = 676. 668 lies between 625 and 676 and is not equal to 676, so 668 is not a perfect square. Step 4: Check 992. Nearby squares: 31^2 = 961, 32^2 = 1024. 992 lies between 961 and 1024 and is not equal to either, so 992 is not a perfect square. Step 5: Therefore, among the four given numbers, only 576 is a perfect square, while 794, 668 and 992 are not.

Verification / Alternative check:
To verify, you can factor 576 completely: 576 = 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3. Grouping equal factors: 576 = (2 * 2 * 2 * 3) * (2 * 2 * 2 * 3) = 24 * 24 = 24^2. For the other numbers, no such clean pairing into identical groups of factors is possible without producing fractional factors. This confirms that only 576 has the structure of a perfect square.

Why Other Options Are Wrong:
794 is not special because it is not a perfect square; it lies between 784 and 841. 668 is not special because it lies between 625 and 676 and is not equal to 676, so it is not a square. 992 is not special because it lies between 961 and 1024 and does not equal any perfect square. 576 stands out because it exactly equals 24^2.

Common Pitfalls:
A typical pitfall is to rely purely on digit patterns or divisibility instead of checking whether the number is a perfect square. Some students may confuse 576 with nearby values or misremember its square root. Another mistake is to factor partially and stop early, missing the perfect square structure. Systematic checking using known squares around each number avoids this problem.

Final Answer:
The only perfect square in the list and therefore the odd one out is 576.