Prove that 3+2V5 is irrational.
Solution Let us assume on the contrary that 3+2/5 is rational. Then there exist co-prime positive integers a and b such that 3+25 a - 35 = 215=-3 5 = 15 = 9-35 2b = V5 is rational a-36 :. a,b are integers is a rational This contradicts the fact that 15 is irrational. So, our supposition is incorrect. Hence, 3+2/5 is an irrational number.
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