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# 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.

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/anQ.

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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Question

A

B

C

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 is

a. 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 1NCERT 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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The decimal expansion of the rational number 14587/ 1250 will terminate after: (A) one decimal place . . . .

The values of the remainder r, when a positive integer a is divided by 3 are 0 and 1 only.Justify yo . . . .

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Mohammed 8 day ago

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