The term "radical" in mathematics typically refers to the first definition you provided: a mathematical expression indicating a root by means of a radical sign. For example, the square root of a number is written using the radical sign (√).
The other definitions you mentioned correspond to:
- A number that cannot be expressed as a ratio of two integers: This defines an irrational number.
- A number that can be expressed as a ratio of two integers with a nonzero denominator: This defines a rational number.
- Indicates how many times the base is used as a factor: This describes the concept of an exponent.
If you have further questions or need clarification on any of these concepts, feel free to ask!