Question

The product of a rational and irrational number is ___ rational

Answer 1

the products of a rational number and irrational number is irrational number

Answer 2

an irrational number unless the rational number is zero

Explanation:

The only case when a product of a rational number times an irrational gives a rational number, is when the rational number is zero. Otherwise the product will always be irrational. The product of an irrational number that cannot be written as a quotient , times another one that can be expressed as a quotient will remain with the characteristic of not being able to be expressed as a quotient.