Prove and apply properties of sums and products involving rational and irrational numbers.
MATHEMATICS · Multi-part · CBSE · Mathematics · Real Numbers · Real Numbers
Problem
Prove and apply properties of sums and products involving rational and irrational numbers.
(i) Prove that the sum of a rational number and an irrational number is always irrational.
(ii) Prove that the product of a non-zero rational number and an irrational number is irrational.
(iii) Using the above results, determine whether the number 32−5 is rational or irrational. Justify your answer.