Question

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

Answer 1

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