Question

show that 2 + root 3 is an irrational number

Answer 1

we need to prove here 2+√3 is irrational no.
let 2+√3 be rational .

then 2+√3 can be written as
   2+√3=a/b     where a and b are integer and b≠0

  √3=a/b-2

√3=a-2b/b

here√3 is irrational  and a-2b/b is rational. hence it arises contradiction that 2+√3 is rational . so our assumption went wrong

therefore,2+√3 is irrational