This is the basic and conceptual question from real numbers in which we have given a number 1/√3 and we have to show that the given number is a irrational number

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 1D, question no 4

## Let us assume that 1/√3 is rational

⇒1/√3×√3/√3=√3/3 is rational

which is only possible if 1/3 is rational and √3 is rational. as we know that, product of two rational numbers is rational.

But the fact is √3 is an irrational

Which is contradictory to our assumption.

which implies 1/√3 is irrational. hence proved.