Which of the following statements is false?
select one:
a. the sum of two rational numbers is always rational.
b. the product of a nonzero rational number and an irrational number is always irrational.
c. the product of two rational numbers is always rational.
d. the sum of two irrational numbers is always rational.

Alright. So We Need To Take A Look At The Answer Choices. The Sum Of Two Rational Numbers Is Always Rational. This Is True. You Cant Add Bad With Bad And Get Good. So You Will Always Get Rational Numbers, So It Is Not A. 

Lets Look At B. The product of a nonzero rational number and an irrational number is always irrational. This is True. Pi Times Any Number Is Irrational. If You Have A Repeating Decimal,You Can't Change It To A Whole Number.

Lets Look At C. The product of two rational numbers is always rational. This Is True. Any Rational Numbers Multiplied Will Always Be Rational. 3.5 * 4 = 14. this Is Still Rational, So Not C.

Lets Look At D. The sum of two irrational numbers is always rational.This Is Not True. If You Do: Pi + Pi, This Will Not Be Rational. So, It Is D.

So, Having Looked At All The Choices, The Answer Is D.