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Prove that the following number is irrational: 2+√5

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One of the most important and conceptual question from real numbers in which we have given a number 2+√5 and we have to show that the given number is a irrational number.

Kindly solve the above problem

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


1 Answer

  1. Let us assume that (2+√5)
    is rational

    Subtract given numbers from 2, considering 2 is rational number as we know,difference of two rational numbers is rational.

    (2+√5) is rational

    but √5 is irrational
    Which is contradictory to our assumption.

    So(2+√5) is an irrational.

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