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 of a circle is calculated as \(2 \times \text{radius}\), and if the radius is an irrational number (for example \(\sqrt{2}\)), the diameter will also be irrational. Additionally, computations involving circles often lead to irrational numbers due to the use of \(\pi\).