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Prove that the following number is irrational: 3√7

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One of the most important and exam oriented question from real numbers in which we have given a number 3√7 and it is already asked in various examinations and we have been asked to prove that the given number is a irrational number.

Kindly solve the above problem in detail

RS Aggarwal, Class 10, chapter 1D, question no 3(vi)


1 Answer

  1. 3√7

    let us assume that 3√7 is rational.

    as we know, product of two rational numbers is rational.

    but 7 is irrational , which is contradictory to our assumption.

    SO 3√7 is irrational.

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