Prove that the reciprocal of an irrational number is irrational.

Question

KnowledgeBoat · Accepted Answer

Let us consider, x as an irrational number. Reciprocal of x is . Let us consider to be a non-zero rational number. Then, will also be an irrational number as product of non-zero rational number and an irrational number is also an irrational number. But = 1 is a rational number. Hence, our supposition is wrong. So, is an irrational number.

Mathematics

Prove that the reciprocal of an irrational number is irrational.

Rational Irrational Nos

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