Let R and I are rational number and irrational number respectively.Assume that sum of R and I is a rational number and equal to PSo\xa0R + I =Por I =P – R……., (1)As P and R both are rational number so P – R is also a rational number.Hence from (1) I is a rational numberBut this contradict that\xa0I is an irrational number.This contradiction has come because we assumed that R+ I is a\xa0rational number.Therefore the sum of irrational number and rational number is always an irrational number.