The measurement that will require the use of irrational numbers is:
the diagonal of one of the cube’s faces.
To explain, while the volume, surface area, and area of the cube’s face can all be calculated using rational numbers when the edge length is a rational number, the diagonal of one of the cube’s faces can be found using the Pythagorean theorem. The formula for the diagonal \(d\) of a square face with edge length \(a\) is given by:
\[ d = a\sqrt{2} \]
Since \(\sqrt{2}\) is an irrational number, the diagonal will also be irrational if the edge length \(a\) is a rational number.
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