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Prove that 1/√3 is a irrational number.

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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


1 Answer

  1. 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.

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