Final answer:
The question asks to identify perfect squares from a given list of numbers and select an additional perfect square from the provided options. Upon analysis, 1, 9, 16, and 625 are identified as perfect squares from the list. All the options (25, 36, 49, 64) are also perfect squares.
Step-by-step explanation:
The student's question revolves around identifying which of the numbers listed (5, 9, 24, 16, 20, 1, 116, 625) are perfect squares and then choosing the number from the given options (25, 36, 49, 64) that also fits the designation of a perfect square. A perfect square is a number that can be expressed as the product of an integer with itself. For example, 9 is a perfect square because it can be written as 3×3. Here, out of the listed numbers, 1 (1×1), 9 (3×3), 16 (4×4), and 625 (25×25) are perfect squares. Looking at the available options, we can see that:
- 25 is 5×5,
- 36 is 6×6,
- 49 is 7×7,
- 64 is 8×8.
All of these are perfect squares as well. Therefore, the question "What's your perfect squares check out at 5, 9, 24, 16, 20, 1, 116, 625?" is asking which numbers among the options a) 25, b) 36, c) 49, and d) 64 would continue the pattern of perfect squares observed in the original list.