NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 1: Real Numbers - Exercise 1.1 - Multiple Choice Questions
Question 8

Question.  8

The product of a non-zero rational and an irrational number is

(A)

always irrational

(B)

always rational

(C)

rational or irrational

(D)

one

Handwritten Notes

The product of a non-zero rational and an irrational number is 1
The product of a non-zero rational and an irrational number is 2
The product of a non-zero rational and an irrational number is 3
The product of a non-zero rational and an irrational number is 4

Video Explanation:

Detailed Answer with Explanation:

Let \(r \neq 0\) be a rational number and \(\alpha\) an irrational number.

If their product \(r\alpha\) were rational, then dividing it by the non-zero rational \(r\) would give \(\alpha = \dfrac{r\alpha}{r}\), which would make \(\alpha\) rational. This is a contradiction.

Hence, the product is always irrational.

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