Prove that 2+√3 is an irrational number , given that √3 is irratio

1.	Prove that 2+√3 is an irrational number , given that √3 is irrational number.
Answer» Let\'s suppose 2+√3 be rationalSince 2+√3 - 2 also be rational ( difference of two rational number is rational ) Now 2+√3 - 2 = √3 which is rationalBut this contradicts the fact that √3 is irrationalThe contradiction arises by assuming √3 rationalTherefore; 2+√3 is irrationalHence proved .

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