I need help asap 1/2k=20

An appliance store sells lamps at $95.00 for two. a department store sells similar lamps at 5 for $250.00. which store sells at a better rate

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?

Having a hard time understanding this question (see attachment).