What type of number is π + 2?
Answer and explanation
Correct answer: Irrational number
The governing concept is that adding a rational number to an irrational number always gives an irrational number. Here π is irrational, while 2 is rational because it can be written as 2/1. Suppose π + 2 were rational. Subtracting the rational number 2 from it would then make π rational, contradicting the known property of π. Therefore π + 2 is irrational, so option B is correct. It is not an integer or a terminating decimal, because every integer and every terminating decimal is rational. The fraction 22/7 is only a rational approximation to π, not its exact value, so replacing π by 22/7 would incorrectly change the classification.
Frequently asked questions
What is the correct answer to this question?
Irrational number
Why is this the correct answer?
The governing concept is that adding a rational number to an irrational number always gives an irrational number. Here π is irrational, while 2 is rational because it can be written as 2/1. Suppose π + 2 were rational. Subtracting the rational number 2 from it would then make π rational, contradicting the known property of π. Therefore π + 2 is irrational, so option B is correct. It is not an integer or a terminating decimal, because every integer and every terminating decimal is rational. The fraction 22/7 is only a rational approximation to π, not its exact value, so replacing π by 22/7 would incorrectly change the classification.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Irrational numbers.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
