Question

The reciprocal of an irrational number is _________​

Answer 1

reciprocal of any irrational number is irrational. Proof: Let x be an irrational number. Then 1/x = a/b where a and b are integers, a ≠ 0 (since 0 is a rational number) and b ≠ 0. x = 1/1/x = 1/a/b = b/a where b and a are integers and a ≠ 0.