Step 1: Understanding the Question:
We need to find the number that does not follow the mathematical pattern shared by the other four numbers.
Step 2: Detailed Explanation:
Analyzing the numbers:
- \(125 = 5 \times 5 \times 5 = 5^3\) (It is a perfect cube)
- \(216 = 6 \times 6 \times 6 = 6^3\) (It is a perfect cube)
- \(343 = 7 \times 7 \times 7 = 7^3\) (It is a perfect cube)
- \(512 = 8 \times 8 \times 8 = 8^3\) (It is a perfect cube)
Analyzing 728:
The next perfect cube after \(8^3\) is \(9^3 = 9 \times 9 \times 9 = 729\).
The number provided is 728, which is \(729 - 1\) or \(9^3 - 1\).
Conclusion: Numbers 125, 216, 343, and 512 are all exact perfect cubes of consecutive integers (5, 6, 7, and 8). Number 728 is not a perfect cube; it is one less than a perfect cube.
Step 3: Final Answer:
728 is the odd one out because it is not a perfect cube.