Which option shows only irrational numbers?
Answer and explanation
Correct answer: √2, √7, π
Option A contains √2, √7, and π. Since 2 and 7 are not perfect squares, √2 and √7 are irrational. The constant π is also irrational, so every number in option A is irrational. In option B, √4 = 2, which is rational, so that set is not exclusively irrational. In option C, 0.25 = 1/4 is rational, despite √3 and √5 being irrational. In option D, 2/3 is rational, although π and √11 are irrational. Therefore option A is the only option containing only irrational numbers. The governing check is to identify roots of non-perfect squares, recognise π as irrational, and distinguish terminating decimals or ratios of integers, which are rational. A single rational member is enough to reject an entire option.
Frequently asked questions
What is the correct answer to this question?
√2, √7, π
Why is this the correct answer?
Option A contains √2, √7, and π. Since 2 and 7 are not perfect squares, √2 and √7 are irrational. The constant π is also irrational, so every number in option A is irrational. In option B, √4 = 2, which is rational, so that set is not exclusively irrational. In option C, 0.25 = 1/4 is rational, despite √3 and √5 being irrational. In option D, 2/3 is rational, although π and √11 are irrational. Therefore option A is the only option containing only irrational numbers. The governing check is to identify roots of non-perfect squares, recognise π as irrational, and distinguish terminating decimals or ratios of integers, which are rational. A single rational member is enough to reject an entire option.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Irrational numbers.
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