Question

prove that 5+2√3 is an irrational number

Answer 1

let 5+2√3 be a rational number and can be expressed in the form
5+2√3=a/b (where a & b are coprime)
2√3=a/b-5
2√3=a-5b/b
√3= a-5b/2b
√3 is rational
This contradicts the √3 is irrational
Therefore, 5+2√3 is irrational