prove that  \frac{3 }{ \sqrt{5} } is irrational. ​

Question

prove that
 \frac{3 }{ \sqrt{5} }
is irrational. ​

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Isabelle 2 weeks 2021-10-08T05:08:42+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-10-08T05:10:41+00:00

    Let 3/root5 be a rational number

    3/root5 = a/b , where a & b are co-prime

    root5= a/b-3

    root5=a-3b/b

    so a ,b and -3 are integers ,we get that root5 is rational and also a-3b/b is rational. But , this contradicts the fact root5 is irrational

    Therefore 3/root 5 is irrational

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