Prove that the product of a nonzero rational number together with an irrational number is an irrational number.

Question

Mathematics

Lorenzo Dean

9 July, 16:16

Prove that the product of a nonzero rational number together with an irrational number is an irrational number.

+3

Answers (1)

Know the Answer?

Taniya Ramos · Answer 1

Each time they assume the sum is rational; however, upon rearranging the terms of their equation, they get a contradiction (that an irrational number is equal to a rational number). Since the assumption that the sum of a rational and irrational number is rational leads to a contradiction, the sum must be irrational.