Question

here's a question. prove (2+root 3) is an irrational number

Answer 1

let us assume to the contrary that 2+root3 is rational. i.e. a and b are coprimes where b is not equal to 0. such that
2+root3=a/b
therefore 
2- a/b= root3
root3=2 - a/b
root3=(2b-a) / b
since a and b are integers so
2-a/b is rational and so root 3 is irrational
but this contradicts the fact that root 3 is irrational
this contradiction has arisen due to our incorrect assumption that 2+root3 is rational
therefore 2+root3 is rational