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Prove that (4-5√2) is a irrational number.

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This is the basic and conceptual question from real numbers chapter in which we have given a number (4-5√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 8


1 Answer

  1. Let us assume that (45√2) is rational .

    Subtract given number from 4, considering 4 is rational number. as we know difference of two rational numbers is rational.

    4(45√2)is rational

    5√2 is rational

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

    As we know prouduct of two rational number s rational
    But the fact is √2 is an irrational.

    Which is contradictory to our assumption.

    Hence, 45√2 is irrational . hence proved.

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