If B = {x ∈ ℕ : x is a factor of 36 and x is a perfect square}, then what is B?
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Answer and explanation
Correct answer: B = {1, 4, 9, 36}
The positive factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36. We now retain only those factors that are perfect squares. Among them, 1 = 1², 4 = 2², 9 = 3² and 36 = 6². The number 16 is not a factor of 36, and 6 is not a perfect square. Therefore, B = {1, 4, 9, 36}, making option A correct.
Frequently asked questions
What is the correct answer to this question?
B = {1, 4, 9, 36}
Why is this the correct answer?
The positive factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36. We now retain only those factors that are perfect squares. Among them, 1 = 1², 4 = 2², 9 = 3² and 36 = 6². The number 16 is not a factor of 36, and 6 is not a perfect square. Therefore, B = {1, 4, 9, 36}, making option A correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
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