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A day full of math games & activities. Find one near you.

Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer by an example

Solution:

Consider x = 2 which is rational

y = √2 which is irrational

The product x × y = 2 × √2 = 2√2 which is irrational

Let us take x = 0 which is rational

y = √2 which is irrational

The product x × y = 0 × √2 = 0 which is rational

Therefore, xy is irrational always if the rational number is not zero.

✦ Try This: The value of (√20 + √80)/(√30 + √10) is equal to

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1

NCERT Exemplar Class 9 Maths Exercise 1.2 Problem 2

Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer by an example

Summary:

The statement “Let x be rational and y be irrational. Is xy necessarily irrational” is true only if the rational number is not zero

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