proove that 5 + 2√5 is irrational

1.	proove that 5 + 2√5 is irrational
Answer» Let 5+2√5 be a rational number = p/qWhere p and q are coprime numbers & q≠0So 5+2√5 = p/q2√5 = (p-5q)/q=> √5 = (p-5q)/(2q)Since RHS is a rational number => √5 is a rational numberBut it contradicts the fact i.e.√5 is irrational numberTherefore our assumption was incorrect=> 5+2√5 is an irrational numberHence proved

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