Final answer:
Subsets R and I consist of real numbers, but R includes rational numbers and zero, while I only includes irrational numbers derived from square roots that are non-repeating and non-terminating.
Step-by-step explanation:
The question prompts us to justify the reason for the members of subsets R and I and to explain their similarities and differences. Subset R consists of the numbers {0, -7, 0.83, 8, ¾, 7/2, 22/7}. These are all real numbers, which include whole numbers, fractions, decimals, and can also be negative or positive.
Subset I contains the numbers {√289, √24, √256}. These are all irrational numbers as they cannot be precisely expressed as a simple fraction and their decimal expansions are non-repeating and non-terminating.
The similarity between the two subsets is that both consist of numbers that can be placed on the number line; they're both subsets of the set of real numbers. The difference is that Subset R includes rational numbers and zero, which can be expressed as fractions or decimals that either terminate or repeat. Subset I, on the other hand, only contains irrational numbers derived from square roots that do not result in rational numbers.