Question

Prove that 2 root3-1 is an irrational number

Answer 1

let assume 2√3-1 is rational
2√3-1=p/q (p,q are integers)
2√3=p/q+1
2√3=(p+q)/q
√3=(p+q)/2q
here RHS is rational but LHS is irrational
contradiction arises
so our assumption rational number is wrong
so 2√3-1 is irrational