Question

prove √3+√5 is rational ​

Answer 1

Suppose √3 - √5 is a rational number say x. Then we have (√3-√5)^2 = x^2 => 8–2√15 = x^2 => 8-x^2 = 2√15. Here, LHS is rational while RHS is irrational. Hence we arrive at a contradiction.