When programming a spreadsheet to handle calculations involving $n$th roots ($\sqrt[n]{a}$), which of the following scenarios will cause the system to return an error because the result is NOT a real number?

A technician is calibrating a calculation engine for a precision measuring device. The device uses $n$th roots ($\sqrt[n]{a}$) to determine material tolerances. Match each mathematical expression with the correct description of its result in the real number system.

True or False: When evaluating the expression $\sqrt[n]{a}$ in a technical computing environment, the result will be a real number for a negative value of $a$ if the index $n$ is an odd integer.

Technical Documentation for nth Root Constraints

You are writing technical documentation for a proprietary calculator app used by your engineering team. You must note that the mathematical expression $\sqrt[n]{a}$ will successfully evaluate to a real number for negative values of the radicand $a$ only when the index $n$ is an ____ number.

Debugging a Risk Calculation Engine

An operations analyst is setting up an automated quality-control script that evaluates algebraic formulas used in inventory forecasting. One key formula uses $n$th roots ($\sqrt[n]{a}$) to determine restocking thresholds. To prevent the program from crashing due to non-real number errors, the analyst must implement a logical validation checklist. Arrange the following steps in the correct order to show the sequence of checks the system must run to determine if the expression $\sqrt[n]{a}$ successfully evaluates to a real number.