A space diagonal of the unit <cube> has displacement <vector> $(1,1,1)$. Its Euclidean <norm>, or two successive applications of the <Pythagorean theorem>, gives
$$
\boxed{d=\sqrt{1^2+1^2+1^2}=\sqrt3\text{ units}.}
$$
The requested diagonal joins opposite vertices; $\sqrt2$ would be the diagonal of a face.

Solution

Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2018 / Paper 1 / 6 / a / Solution

 Solution (source code)