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Prove that the following number is irrational: (2-3√5)

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One of the most important and conceptual question from real numbers in which we have given a number (2-3√5) and it was already asked in previous year papers 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 3(viii)


1 Answer

  1. Let us assume that (23√5) is rational.

    subtract given numbers from 2 , considering 2 is rational number.
    as we know , difference of two rational numbers is rational
    2(23√5)is rational.

    35 is rational

    above result is possible if 3 is rational and 5 is rational.
    Because , product of two rational numbers is rational.

    but the fact is 5 is an irrational .

    Our assumption is wrong, and (23√5) is irrational

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