Which is the roster form of T = {x ∈ ℕ : x is a perfect square and x < 50}?
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Answer and explanation
Correct answer: {1, 4, 9, 16, 25, 36, 49}
The positive perfect squares are obtained by squaring natural numbers: 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25, 6² = 36, and 7² = 49. The next square, 8² = 64, is not less than 50. Under the convention ℕ = {1,2,3,...}, zero is not included. Hence T = {1, 4, 9, 16, 25, 36, 49}.
Frequently asked questions
What is the correct answer to this question?
{1, 4, 9, 16, 25, 36, 49}
Why is this the correct answer?
The positive perfect squares are obtained by squaring natural numbers: 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25, 6² = 36, and 7² = 49. The next square, 8² = 64, is not less than 50. Under the convention ℕ = {1,2,3,...}, zero is not included. Hence T = {1, 4, 9, 16, 25, 36, 49}.
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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