These are important terms and notations for this section.

Radical (expression) A mathematical expression comprised of a radical symbol and a
radicand.

**For Example:**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 , the 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 writing as part of the radical
symbol. Specifically it is the exponent that the radical cancels.

**For Example:**In the radical expression , the root-value is .Radicand The content contained inside of a radical symbol.

**For Example:**In the radical expression , the is the radicand.Inverse Function If is a function, then an inverse function is another function,
(commonly denoted as ) such that

Type 1 Radical Type one radicals have radicands that are entirely factored, meaning
that each term of the radicand is multiplied against the other terms of the
radicand. There are no addition or subtraction signs between terms in the
radicand.

**For example:**The radical is a type one radical because each of its terms are multiplied against the other terms. Specifically, the only addition or subtraction symbols are*inside*terms, and each term is surrounded by parentheses (implicitly or explicitly).Type 2 Radical Type two radicals have radicands that are

**not**entirely factored, meaning that there are terms in the radicand that are separated by addition or subtraction symbols.**For example:**The radical is a type two radical because not all its terms are multiplied against the other terms. Specifically, there are terms that are being added or subtracted to the other terms (in this case, the is a term being subtracted from the other term(s) ).