Question

Show that the sum of two irrational numbers can be rational or irrational. Provide two examples of each.

Answer 1

Pi is irrational, but 2-Pi is also irratonal. Let a = Pi and b=2-Pi. In this example a+b=2 which is rational.
Other example is a=3.2437629... ad Infinitum and b=6.756230... where the digits all sum to 9 therefore make a+b=10