Question

1by √2 these rational or irrational

Answer 1

it is irrational because as √2 is irrational so 1/√2 is also irrational

Answer 2

Let us assume that 1/2+root 3 is rational .So 1/2+root 3 = a/b where a and b are irrationals.Now arranging the equation we get 1=a/b * 2+root 3so root 3 = 1-a/b -2since rhs is a rational number root 3 should be also rational .But this contradicts the reality that root 3 is irrational .So our assumption is wrong and hence we conclude that is irrational