KnowledgeBoat Logo

Mathematics

Prove that the reciprocal of an irrational number is irrational.

Rational Irrational Nos

16 Likes

Answer

Let us consider, x as an irrational number.

Reciprocal of x is 1x\dfrac{1}{x}.

Let us consider 1x\dfrac{1}{x} to be a non-zero rational number.

Then, x×1xx × \dfrac{1}{x} will also be an irrational number as product of non-zero rational number and an irrational number is also an irrational number.

But x×1xx × \dfrac{1}{x} = 1 is a rational number.

Hence, our supposition is wrong. So, 1x\dfrac{1}{x} is an irrational number.

Answered By

7 Likes


Related Questions