If R = {x ∈ ℕ : x is a divisor of 36 and x is a perfect square}, which of the following is R?
Answer and explanation
Correct answer: R = {1, 4, 9, 36}
The positive divisors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. We must retain only those divisors that are also perfect squares. Here, 1 = 1², 4 = 2², 9 = 3², and 36 = 6². The numbers 2, 3, 6, 12, and 18 are not perfect squares. Therefore, the required set is R = {1, 4, 9, 36}, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
R = {1, 4, 9, 36}
Why is this the correct answer?
The positive divisors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. We must retain only those divisors that are also perfect squares. Here, 1 = 1², 4 = 2², 9 = 3², and 36 = 6². The numbers 2, 3, 6, 12, and 18 are not perfect squares. Therefore, the required set is R = {1, 4, 9, 36}, so option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
