Question

Prove that the reciprocal of an irrational number is irrational. USING ALGEBRA.

Answer 1

Step-by-step explanation:

Let a be the irrational number in question and let b be the inverse of this number.

Suppose that b is in the rational numbers, or that m/n = b where m and n are integers and gcd(m,n) = 1. Then the inverse of b is n/m which is in the rational numbers but the inverse of b is a and a is in the irrational numbers. This tells us that a is rational and irrational which is a contradiction so b must be irrational.

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