Final answer:
The difference between the two square numbers in the list is option A) 1. The difference between the two cube numbers in the list is option D) 216.
Step-by-step explanation:
In the given list, the difference between two square numbers is calculated by subtracting the smaller square from the larger square. The options A) 1, B) 4, C) 9, and D) 16 are all square numbers. Let's calculate the differences:
- Difference between 4² and 1² = 16 - 1 = 15
- Difference between 9² and 4² = 81 - 16 = 65
- Difference between 16² and 9² = 256 - 81 = 175
Therefore, the difference between the two square numbers in the list is option A) 1.
Similarly, to calculate the difference between the two cube numbers in the list, we subtract the smaller cube from the larger cube. The options A) 27, B) 64, C) 125, and D) 216 are all cube numbers. Let's calculate the differences:
- Difference between 27³ and 64³ = 19683 - 262144 = -242461
- Difference between 64³ and 125³ = 262144 - 1953125 = -1690981
- Difference between 125³ and 216³ = 1953125 - 10077696 = -8124567
Therefore, the difference between the two cube numbers in the list is option D) 216.