Final answer:
The principal nth root of a real number is the non-negative root. It is the root that is commonly used in equations, graphing functions, and in the discussion of domains and ranges.
Step-by-step explanation:
The principal nth root of a real number is the non-negative root of the real number. When you take the nth root of a number, there can be multiple solutions, but the principal root is the one that is non-negative. This is relevant when dealing with even roots, like square roots or fourth roots, etc. For example, the square root of 9 is ±9, but the principal square root is 3, which is the positive root.
This becomes important in primary equations where the principal root is assumed, avoiding the complexity of dealing with negative roots unless specifically indicated. It's especially relevant in the context of graphing functions or when discussing domains and ranges of those functions.