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Show that 3√2 is not a …

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Show that 3√2 is not a irrational

    • Posted by Vishalini Singar 5 years, 3 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Yogita Ingle 5 years, 3 months ago

    Let us assume, to the contrary, that 3 √ 2​ is 

    rational. Then, there exist co-prime positive integers a and b such that

    3 √ 2​= a/b

    ⇒  √ 2 ​= a/3b 

    ⇒  √ 2​ is rational       ...[∵3,a and b are integers∴ 1/3b ​is a rational number]

    This contradicts the fact that  √ 2​ is irrational. 

    So, our assumption is not correct.

    Hence, 3 √ 2​ is an irrational number.

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