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Prove that root 2 is an …

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Prove that root 2 is an irrational no

    • Posted by Deepak Yadav 3 years, 5 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Emaan Arora 3 years, 5 months ago

    Let √2 is an irrational number Let √2=p/q (where p and q are integers and q is not equal to 0) -1 Let a/b is the lowest form of p/q So,p/q=a/b (where a and b are co- prime numbers) Putting in 1 √2=a/b Squarring both side (√2)^2 = (a/b)^2 2=a^2/b^2 a^2 = 5b^2 So,2 is the factor of a^2 also 2 is the factor of a Let a=2m( where m is some integer) (2m)^2= 2b^2 4b^2=2b^2 4b^2/2 = b^2 2b^2 = b^2 b^2=2b^2 So,2 is the factor of b^2 also 2 is the factor of b Here,2 is the factor of both a and b .This contradict our supposition that √2 is an rational number is wrong. Hence ,√2 is an irrational number

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