Question

Which number gives you an irrational product when you multiply it by 2

Answer 1

Explanation:

An irrational number is a number that can't be written as a simple fraction while a rational number is a number that can be written as the ratio of two integers, that is, as a simple fraction. So in this case we have the number 2 which is ration, and we can multiply it by an irrational number $n$ such that the product is an irrational number. So any irrational number will meet our requirement because the product of any rational number and an irrational number will lead to an irrational number. For instance:

$\bullet \ 2\sqrt{2} \\ \\ 2 \ is \ rational \\ \\ \sqrt{2} \ is \ irrational \\ \\ 2\sqrt{2} \ is \ irrational \\ \\ \\ \bullet \ 2\pi \\ \\ 2 \ is \ rational \\ \\ \pi \ is \ irrational \\ \\ 2\pi \ is \ irrational$