prove that 3 √2 is an irrational number​

Question

prove that 3 √2 is an irrational number​

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Genesis 2 months 2021-10-09T19:00:42+00:00 2 Answers 0 views 0

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    0
    2021-10-09T19:01:46+00:00

    as √2 is an irrational number , we multiply 3 to √2 then it also becomes an irrational number

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    2021-10-09T19:02:08+00:00

    Answer:

    let us assume that 3√2 is rational

    Then we have two integers a and b such that:

    3√2=a/b

    √2=a/3b

    a,b and 3 are integers,hence a/3b is rational

    Since a/3b is rational

    hence√2 is rational

    But this contadicts the fact that √2 is irrational.

    This contradiction has arisen due to our incorrect assumption that 3√2 is rational.

    Hence 3√2 is irrational

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