Final answer:
To solve this puzzle, we need to find square and cube numbers less than or equal to 100 that can fill in the circles and make the sums true. The first circle can be filled with 64 and the second circle can be filled with 27.
Step-by-step explanation:
To solve this puzzle, we need to find square and cube numbers less than or equal to 100 that can fill in the circles and make the sums true. Let's start by looking at the given circles: (36) + (___) and (64) + (___).
For the first circle, we need a square number that, when added to 36, gives a sum equal to a cube number. The only square number less than or equal to 100 that satisfies this condition is 64. Therefore, the first circle can be filled with 64.
For the second circle, we need a cube number that, when added to 64, gives a sum equal to a square number. The only cube number less than or equal to 100 that satisfies this condition is 27. Therefore, the second circle can be filled with 27.