Which option is correct about the sum of a rational and an irrational number?
Answer and explanation
Correct answer: Always irrational
Let \(r\) be rational and \(x\) be irrational. Then \(r+x\) must be irrational. If \(r+x\) were rational, then \(x=(r+x)-r\) would be the difference of two rational numbers and hence rational, which is a contradiction. For example, \(3+\sqrt{2}\) is irrational. Therefore, option A is incorrect, and the sum is not necessarily an integer either. Exam tip: the sum or difference of a rational number and an irrational number is always irrational.
Frequently asked questions
What is the correct answer to this question?
Always irrational
Why is this the correct answer?
Let \(r\) be rational and \(x\) be irrational. Then \(r+x\) must be irrational. If \(r+x\) were rational, then \(x=(r+x)-r\) would be the difference of two rational numbers and hence rational, which is a contradiction. For example, \(3+\sqrt{2}\) is irrational. Therefore, option A is incorrect, and the sum is not necessarily an integer either. Exam tip: the sum or difference of a rational number and an irrational number is always irrational.
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.
