The real-world problem that is most likely to involve irrational numbers is:
finding the side length of a square based on the area.
The reason is that if the area \( A \) of a square is given, the side length \( s \) can be found using the formula \( s = \sqrt{A} \). If \( A \) is not a perfect square, \( \sqrt{A} \) will be an irrational number.