Prove that “Sum of two irrational numbers is a rational number “

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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 P So\xa0R + I =P or 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 number But 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.