Which of the following statements is false?

a)the product of two rational numbers is always irrational.
b)the sum of a rational number and an irrational number is always irrational.
c)the product of a nonzero rational number and an irrational number is always irrational.
d)the product of two irrational numbers is either rational or irrational.

Answer is statement A.

Product of 2 rational number is always rational. Rational number is number which can be represented as ratio which both numerator and denominator are finite whole numbers. If you multiply 2 finite numbers you wiill get 2 finite numbers.

B is true because infinite + finite is infinite (talking about numerators)

C simillar case as B. infinite * finite is infinite

D is true as well. for example √2*√2 is rational number. it is number 2. while √2*√3 is irational.