A logistics coordinator is updating a facility's floor plan database. One section of a storage bay is recorded with a width of ${}5 + \sqrt{75}$ feet. Which of the following represents this measurement in its most simplified radical form?

As a data analyst for a regional construction firm, you are updating the structural specifications in the company's project database. The system requires all measurements to be entered in their most simplified radical form. Match each original measurement on the left with its correctly simplified version on the right.

A construction supervisor is calculating the length of a metal support brace for a project. The preliminary calculation results in a length of ${}2 + \sqrt{98}$ feet. To communicate the exact specifications to the fabrication team, the supervisor must simplify the expression. Arrange the following steps in the correct order to reach the most simplified radical form.

A technician is documenting the total resistance in a circuit segment as ${}5 + \sqrt{75}$ ohms. After simplifying the radical, the technician records the value as ${}5 + 5\sqrt{3}$ ohms. It is mathematically correct for the technician to further simplify this result to ${}10\sqrt{3}$ ohms by adding the integer and the radical coefficient together.

A quality assurance engineer at a manufacturing plant is standardizing structural measurements in a database. One measurement is initially recorded as ${}5 + \sqrt{75}$ millimeters. After extracting the largest perfect square from the radical to obtain the simplified form ${}5 + 5\sqrt{3}$, the engineer leaves the expression as a sum. The integer ${}5$ and the radical term ${}5\sqrt{3}$ cannot be combined into a single value because they are not ____.