Prove and apply properties of sums and products involving rational and irrational numbers.
a. (i) Prove that the sum of a rational number and an irrational number is always irrational.
b. (ii) Prove that the product of a non-zero rational number and an irrational number is irrational.
c. (iii) Using the above results, determine whether the number 32−5 is rational or irrational. Justify your answer.