Question

Prove √3-1 is irrational

Answer 1

hello Dear

Here is Your Answer

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 3

so root 3 = 1-a/b -2

since 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.

Hope it Heplfull