Question

Which statement is not always true?

Answer 1

A. True. Summing any rational number with an irrational number leads to an irrational result. The proof is a bit lengthy so I'm leaving it out. 

B. True. Adding p/q with r/s leads to (ps+qr)/(qs) which is rational. Keep in mind that q and s cannot be zero.

C. False. One counter example is sqrt(3)*sqrt(12) = sqrt(3*12) = sqrt(36) = 6. This shows the product of two irrational numbers, in this case sqrt(3) and sqrt(12), multiplying to get a rational result 6 = 6/1.

D. True. Multiplying p/q and r/s leads to (p*r)/(q*s) which is rational. Keep in mind that q and s cannot be zero.

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The final answer is choice C