Question

prove that the reciprocal of an irrational number is irrational

Answer 1

as you know ✓5 is irrational number !
so it's reciprocal would be 1/✓5

and you know the value of ✓5=2.32........
1/2.32.....=10000000..../232...
here the expansion of irrational number is no terminating ,and you say the reciprocal of irrational number is aslo irrational.
hope you got it !