Question

prove that (2+√3) is a irrational number​

Answer 1

let (2+√3) be rational.

(2+√3)=a\b [where a and b are coprime numbers, b is not equal to 0]

√3=a\b-2

√3=a-2b\b

here, RHS is rational number and LHS is irrational

LHS is not equal to RHS.

this contradicts to the fact that our assumption is wrong and (2+√3) is irrational.