Radical (expression) A mathematical expression comprised of a radical symbol and a radicand.
For Example: $\sqrt [5]{32}$ is a radical expression.
Note: This is often just referred to as a ‘radical’, where context is used to determine if the symbol or the entire expression is meant.

Radical (symbol) A symbol denoting a root value of the radicand.
For Example: In the radical expression $\sqrt [5]{32}$, the $\sqrt [5]{\text { }}$ is the radical.
Note: This is often just referred to as a ‘radical’, where context is used to determine if the symbol or the entire expression is meant.

Root-value The root-value of a radical is the number written as part of the radical symbol. Specifically it is the exponent that the radical cancels. For Example: In the radical expression $\sqrt [5]{32}$, the root-value is $5$.

Radicand The content contained inside of a radical symbol.
For Example: In the radical expression $\sqrt [5]{32}$, the $32$ is the radicand.

Inverse Function If $f(x)$ is a function, then an inverse function is another function, (commonly denoted as $f^{-1}(x)$) such that $$f^{-1}(f(x)) = f(f^{-1}(x)) = x$$

Extraneous Solution An extraneous solution is a ‘solution’ that is acquired as a result of some solution method, but the solution doesn’t actually satisfy the original problem. See Example 9 in this topic for an example of extraneous solutions.