Which of these is an irrational number between 1 and 3?
Answer and explanation
Correct answer: √5
The governing ideas are the comparison of square roots and the distinction between rational and irrational numbers. Since 1² = 1, 3² = 9, and 1 < 5 < 9, taking positive square roots gives 1 < √5 < 3. Also, 5 is not a perfect square, so √5 is irrational; it cannot be expressed as a ratio of integers and its decimal expansion is non-terminating and non-repeating. Thus option B satisfies both required conditions. The other choices simplify to rational numbers: √9/√9 = 3/3 = 1, 2/2 = 1, and 2.5/2.5 = 1. Each is rational and lies at the lower boundary rather than strictly between 1 and 3. Therefore √5 is the unique correct answer.
Frequently asked questions
What is the correct answer to this question?
√5
Why is this the correct answer?
The governing ideas are the comparison of square roots and the distinction between rational and irrational numbers. Since 1² = 1, 3² = 9, and 1 < 5 < 9, taking positive square roots gives 1 < √5 < 3. Also, 5 is not a perfect square, so √5 is irrational; it cannot be expressed as a ratio of integers and its decimal expansion is non-terminating and non-repeating. Thus option B satisfies both required conditions. The other choices simplify to rational numbers: √9/√9 = 3/3 = 1, 2/2 = 1, and 2.5/2.5 = 1. Each is rational and lies at the lower boundary rather than strictly between 1 and 3. Therefore √5 is the unique correct answer.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Irrational numbers.
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