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Prove that 5√2 is an irrational number.

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One of the most important and conceptual question from real numbers chapter as it was already asked in various important examinations in which we have given a number 5√2 and we have to show that the given number is a irrational number

Kindly give me a detailed solution of this question

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


1 Answer

  1. Let us assume that 5√2is a rational.

    Which is only possible if 5 is rational and √2 is rational.

    as we know product of two rational number is rational.

    But the fact is 2 is an irrational.

    which contradicts our assumption .

    5√2 is an irrational hence proved.

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