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Prove that 2/√7 is an irrational number.

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An important and exam oriented question from real numbers chapter as it was already asked in previous year papers in which we have given a number 2/√7 and we have to prove that the given number is an irrational number

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 1D, question no 11


1 Answer

  1. Let us assume that 2/√7 is rational number.

    2/√7×√7​/√7=2√7/7 is rational number .

    which is only possible is 2√7​/7 is rational and 7 is rational.

    But the fact is √7is an irrational.

    which contradicts to our assumption.

    2/√7 is an irrational number. hence proved.

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