Question

Show that the reciprocal Imp of an irrational number is irrational

Answer 1

Let us take irrational numbers on taking reciprocal on dividing if we can write it in p/q form it's rational but I guess it is top most doubt of getting it I assure you that you cannot get it in p/q form

Answer 2

Answer:

The reciprocal of any irrational number is irrational. 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