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Prove that (2√3-1) is an irrational number.

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This question is taken from real numbers chapter in which we have given a number (2√3-1) and we have to show that the given number is a irrational number

Kindly solve the above problem in detail

RS Aggarwal, Class 10, chapter 1D, question no 7


1 Answer

  1. Let us assume that (231) is rational .
    add 1 to be above number, considering 1 is rational number.

    as we know , sum of two rational numbers is rational.
    Sum = 2√31+1=23

    which is only possible if 2 is rational and 3 is rational.

    But the fact is 3 is an irrational number which contradicts to our assumption .

    So, (2√31) is an irrational.

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