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Prove √2 irrational

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Prove √2 irrational

    • Posted by Shruti Lakra 6 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Swaran Singh 6 months ago

    Let assume that √2 is an rational number and √2/1 = a/b , where a and b are integers and co-prime , b ≠0 . b√2 = a By squaring both sides, we get 2b²= a² _ (1) Here, a² is divisible by 2 and a also divisible by 2. Now , let a=2c , where c is an integer . By squaring both sides, we get a²= 4 c² By Substituting it in eq ( 1) 2b²= 4c² b² = 2c² Here , b² is divisible by 2 , also b is divisible by 2. Therefore, 2 is a common factor of a and b . This contradicts the fact that a and b are not co - prime. Therefore , our assumption is wrong.

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