Prove that the sum of a rational number and an irrational numbet is al

1.	Prove that the sum of a rational number and an irrational numbet is always irrational
Answer» 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.

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