Select the odd number from the given alternatives: 49, 25, 8, and 36.

Introduction / Context:
This is another number classification question where you are asked to pick the odd number out of a set. The pattern here is based on identifying perfect squares and comparing them with a perfect cube. Such problems test knowledge of basic arithmetic properties and your ability to organise numbers into familiar categories like squares and cubes.

Given Data / Assumptions:

• The numbers provided are 49, 25, 8, and 36.
• We expect that three numbers will share one property, such as being perfect squares, while one number will have a different property.
• We assume understanding of perfect squares (n^2) and perfect cubes (n^3) for small integers.
• No advanced mathematics is needed, only knowledge of multiplication tables up to at least 10.

Concept / Approach:
The strategy is to check whether each number can be expressed as the square of an integer or the cube of an integer. 49, 25, and 36 are familiar as square numbers: 7^2, 5^2, and 6^2. Meanwhile, 8 is known as 2^3, a perfect cube and not a square. By identifying this distinction, we can classify three numbers as squares and one number as a cube, making the cube the odd one out.

Step-by-Step Solution:
Step 1: Check 49. We know 7 * 7 = 49, so 49 is a perfect square, equal to 7^2. Step 2: Check 25. We know 5 * 5 = 25, so 25 is a perfect square, equal to 5^2. Step 3: Check 36. We know 6 * 6 = 36, so 36 is a perfect square, equal to 6^2. Step 4: Check 8. We know 2 * 2 * 2 = 8, so 8 is a perfect cube, equal to 2^3, and not a square. Step 5: Group 49, 25, and 36 as perfect squares of integers. Step 6: Recognise that 8 is different because it is a cube and not a square. Step 7: Conclude that 8 is the odd number among the given alternatives.

Verification / Alternative check:
To verify, list the squares of integers: 5^2 = 25, 6^2 = 36, and 7^2 = 49, all appearing in the options. Next, list small cubes: 2^3 = 8, 3^3 = 27, and so on. Only 8 from this cube list appears among the options. Thus, three options clearly appear in the square list and one in the cube list. This classification confirms that 8 is the only cube and therefore the odd one out.

Why Other Options Are Wrong:
49 is a perfect square (7^2) and fits the square number pattern along with 25 and 36, so it is not the odd one out.
25 is also a perfect square (5^2) and belongs to the same category as 49 and 36.

36 is another perfect square (6^2) and clearly matches the group of square numbers, so it cannot be the different choice.

Common Pitfalls:
A common mistake is to focus on parity, that is, whether numbers are even or odd. Here 49 and 25 are odd while 8 and 36 are even, which does not give a single unique odd one out. Another mistake is to confuse 8 with 9, because 9 is a square (3^2) while 8 is not. To avoid such errors, it is useful to memorise both squares and cubes of small integers. This knowledge helps you quickly classify numbers and select the correct option in odd one out questions without guesswork.

Final Answer:
The odd number is 8.