The real-world problem most likely to involve irrational numbers is finding the diameter of a circle based on the radius. This is because the diameter is calculated using the formula \(d = 2r\), where \(r\) can be any real number, including irrational numbers. More generally, calculations involving circles, such as determining circumference or area, often yield irrational numbers (like \(\pi\)).
Another relevant option is finding the side length of a square based on the area, particularly when the area is not a perfect square, which can also lead to irrational numbers.
However, among the options provided, the diameter of a circle based on the radius is the most direct association with irrational numbers due to its inherent relation to \(\pi\).