The real-world problem that is most likely to involve irrational numbers is:
finding the side length of a square based on the area.
This is because the side length is calculated using the square root of the area, and the square root of a number that is not a perfect square is an irrational number. For example, if the area of the square is 2, the side length would be \(\sqrt{2}\), which is an irrational number.