Question

Prove or disprove that the product of two irrational numbers is irrational.

Short answer

When two irrational integers are multiplied, the result is not always irrational.

Step-by-step solution

Introduction

Need to disprove that the multiplication of two irrational numbers is irrational.

This means, when two irrational integers are multiplied, the result is not always irrational.

To disprove this, give a counter example.

Counter example

Let\(a = \sqrt 3 = b\)be a nonzero irrational number.

Then\(a.b = \sqrt 3 .\sqrt 3 \)

\( = 3\)is rational number.

Thus, when two irrational integers are multiplied, the result is not always irrational.