The index of a radical is the number that indicates the degree of the root being taken. It is often represented as a small number placed to the upper left of the radical sign.
For example, in the radical expression √x, the index is implicitly 2, meaning we are looking for the square root of x. In contrast, &radic[3]{x} has an index of 3, indicating that we are seeking the cube root of x.
The index tells us how many identical factors are needed to produce the number under the radical. If the index is not specified, it is commonly understood to be 2. This means that when no index is written, we are usually referring to square roots.
In summary, the index of a radical is a crucial part of understanding which root is being calculated, and recognizing it helps clarify the mathematical operation involved.