A technical intern is simplifying a precision measurement for a project report. The measurement is expressed as $\frac{10 - \sqrt{75}}{5}$. Arrange the following steps in the correct chronological order to simplify this expression to its simplest radical form.

A precision machinist is following a blueprint for a custom-built housing that lists a critical gap measurement as $\frac{6 - \sqrt{45}}{3}$ millimeters. To make the measurement more practical for a digital caliper, the machinist simplifies the expression. Which of the following is the correct simplified form of this gap measurement?

A technician at a precision tool manufacturing plant is verifying part dimensions on a blueprint. Match each mathematical component from the expressions $\frac{10 - \sqrt{75}}{5}$ and $\frac{6 - \sqrt{45}}{3}$ with its correct simplified form or common factor used during the simplification process.

An environmental analyst is calculating the radius of a containment zone using the expression $\frac{6 - \sqrt{45}}{3}$. To begin the simplification, the analyst identifies the largest perfect square factor of the radicand 45 to simplify the radical $\sqrt{45}$. This perfect square factor is ____.

A quality control inspector is reviewing a tolerance calculation given as $\frac{10 - \sqrt{75}}{5}$. To correctly simplify this expression, the inspector should first divide the 10 by the 5, resulting in ${}2 - \sqrt{75}$, before simplifying the radical.