Answer:
The product of a non-zero rational number and an irrational number is irrational.
Explanation:
For answer 1, if we take 2(a rational number) and 4(another rational number) and add or sum them together, we get 6. (2+4=6) This is clearly also rational as 6 is rational.
For answer choice 2, it follows the same logic. 2*4=8: 2 and 4 are rational and so is 8.
For answer choice 3, we see that any rational number that is not zero multiplied by an irrational number is irrational. A good example of this would be 2 * π = 2π. 2 is rational and not 0 and pi is irrational. 2π is irrational so answer choice 3 seems to be the answer. Also the reason why it cannot be 0 is because pi*0 = 0 so anything multiplied by 0 will equal 0. 0 is rational so if the answer did not say any rational number but 0, it would have been incorrect.
For answer choice 4 it says that the sum of a rational number and irrational number is rational. This is like saying if one part of a statement is true but the other parts are false that the statement is true. So, if we add 2 to pi, would that be rational or irrational? It would be irrational because we still have that neverending sequence of numbers that are in pi, but plus 2 so 3.14... + 2 = 5.13159....