Question

What will be he product of an irrational number and a non-zero rational number?​

Answer 1

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."

Answer 2

Answer:

By definition, an irrational number in decimal form goes on forever without repeating (a non-repeating, non-terminating decimal). By definition, a rational number in decimal form either terminates or repeats.  

By multiplying a non repeating non terminating number to repeating or terminating/repeating number, the result will always be a non terminating non repeating number.