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Prove under root 2 is a …

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Prove under root 2 is a irrational no.

    • Posted by Aditya Kumar 3 years, 2 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Rishita Bharadwaj 3 years, 2 months ago

    Let √2 be a rational no. in the form a/b, where a and b are integers with no common factors other than 1. :. √2 = a/b => a = √2b => a²= 2b² -----(I) So, 2 is a factor of 2b² and a². Hence, 2 is also a factor of a.----(ii) Again, let 2m=a (where a is an integer) Putting a=2m in (I), (2m)²=2b² => 4m²=2b² => b²=2m² So,2 is a factor of 2m² and b². Hence, 2 is also a factor of b.---(iii) From (ii) and (iii), 2 is the common factor of both a and b. But this is not possible, since a and b has no other factors than 1. :. Our assumption is wrong. √2 is an irrational number.

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