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 relationship between the diameter (d) and the radius (r) of a circle is given by the formula \( d = 2r \). While that itself doesn't involve irrational numbers, the circumference of a circle is given by \( C = 2\pi r \), where \(\pi\) is an irrational number. Therefore, in calculations involving circles, especially when working with areas or circumferences, we often encounter irrational numbers related to circles.