Question

show 2 root 3 minus 1 is irrational number

Answer 1

let us assume that 2√3-1 is rational
⇒2√3-1=p/q
⇒2√3=p/q+1
⇒2√3=p+q/q
⇒√3=p+q/2q
irrational=rational
which is a contradiction
∴our assumption is wrong
2√3-1 is irrational

Answer 2

assume that 2√3-1 is rational number 
 2√3-1= a/b
2√3=a/b+1
add square on both sides 
(2√3)²=(a/b+1)²
12=(a/b)²+2(a/b ) (1 )+1²
12= a/b²+2a/b+1
12=a/b²+3a/b
12=a²+3ab
      -----------
            b²
=a²+3ab
  ------------
    12b²
hence our assume is wrong 
it is a irrational number