Question

Prove that the difference of a rational and an irrational number is always

irrational.​

Answer 1

Answer:

This is how you can prove it always irrational.

Answer 2

If you multiply any irrational number by the rational number zero, the result will be zero, which is rational. Any other situation, however, of a rational times an irrational will be irrational. A better statement would be: "The product of a non-zero rational number and an irrational number is irrational."