Question

Which number produces an irrational number when added to 1/2

Answer 1

Any irrational number when added to 1/2 will give an irrational number.

Take $\pi$

add it :

$\frac{1}{2} + \pi$

$= 0.5 + \pi$   is an irrational number.

You can select any irrational number as far as the decimal digits just go on forever and does not have a repeating cycle.