50) let m be a rational number and n be an irrational number. (m)(n) = c, assume c is rational mn m = c m n = c m , so n is rational, contradicting the initial assumption. the proof shows that the product of an irrational and rational number is explain. a) rational. since an irrational number cannot equal a rational number. b) irrational. since an irrational number cannot equal a rational number. c) rational. since you can write it as the division of two rational numbers. d) irrational. since you can write it as the division of two rational numbers.