Prove that 3 +2√5 is irrational

Prove that 3 +2√5 is irrational let us assume to the contrary that 3+ 2√5 is a rational number. So 3 + 2√5 = p/q , where p and q are coprime integers and q is not equal to zero 2√5 = p/q -3 2√5 = (p-3q)/q √5= (p-3q)/2q since √5 is irrational but (p-3q)/2q … Read more