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Prove that the following number is irrational: 3+√2

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This question is taken from real numbers in which we have given a number 3+√2 and it is also asked in previous year papers and we have to show that the given number is a irrational number.


1 Answer

  1. Let us assume that (3+√2)
    is rational

    Subtract given numbers from 3, considering 3 is rational number as we know,difference of two rational numbers is rational.

    So (3+√2) is rational
    but, √2 is irrational
    Which is contradictory to our assumption.

    So (3+2) is an irrational.

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