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

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## The product of a non zero rational number with an irrational number is always an number.

The product of a non zero rational number with an irrational number is always an number.

Byju's Answer Standard IX Mathematics

Operations on Rational and Irrational Numbers

The product o... Question

The product of a non-zero rational number with an irrational number is always an ________ number.

Open in App Solution

The product of a non-zero rational number with an irrational number always results in an irrational number.

Hence, the product of a non-zero rational number with an irrational number is always an irrational number.

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SIMILAR QUESTIONS

**Q.**The product of a non - zero rational number with an irrational number is always :

**Q.**The product of a non-zero rational number and an irrational number is always a/an

**Q.**

Product of a non-zero rational number and an irrational number is always _______.

**Q.**The product of a non-zero rational number with an irrational number is always an irrational number.

**Q.**

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

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Standard IX Mathematics

## The product of a non

Click here👆to get an answer to your question ✍️ The product of a non - zero rational and an irrational number is

Question

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

**A**

## always irrational

**B**

## always rational

**C**

## rational or irrational

**D**

## one

Medium Open in App

Updated on : 2022-09-05

Solution Verified by Toppr

Correct option is A)

Let x be a rational number and y be an irrational number.Let xy=a.

Let us assume that a is rational.

Since, a is rational it can be expressed as

q p

, where p and q are integers.

Let x= n m

, where m and n are integers.

Now, xy=a n my = q p .

On cross multipliying we get,

⇒y= qm pn .

Now, pn and qm are integers.

Hence, qm pn

is a rational number.

However, y is irrational.

Hence, our assumption is incorrect.

Hence, the product of a non-zero rational and an irrational number is always an Irrational number.

So, option A.

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## The product of a non

The product of a non-zero rational and an irrational number is (A) always irrational, (B) always rational, (C) rational or irrational, (D) one - The product of a non-zero rational and an irrational number is always irrational

The product of a non-zero rational and an irrational number isa. always irrational

b. always rational

c. rational or irrational

d. one

**Solution:**

It is given that,

Product of a non-zero rational and an irrational number is always irrational.

Therefore, the answer is a. always irrational

**✦ Try This:**Is the product of a rational and irrational number always irrational? Give an exampleThe product of rational and irrational numbers is an irrational number

If a is a rational number and b is an irrational number

Then ab is irrational.

Example: a = 2 and b = √3

ab = 2 √3

2 √3 is an irrational number.

Therefore, the product of a rational and irrational number is always irrational

**☛ Also Check:**NCERT Solutions for Class 10 Maths Chapter 1

**NCERT Exemplar Class 10 Maths Exercise 1.1 Problem 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

**Summary:**

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

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