Question

show that 7root3-1 is irrational number

Answer 1

let us assume 7√3-1 is a rational no
7√3-1=a/b where a and b are coprime no
7√3=a/b+1
7√3=a+1/b
√3=a+1/7b
Lhs is an irrational no.........(1)
rhs is a rational no.......(2)
1 and 2 as a rational no≠irrational no 
7√3-1 is not a rational no
∴This contradiction is due to our wrong assumption
∴7√3-1 is an irrational no