Radical
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
A radical is a symbol used to represent the root of a number or expression. The most common radical is the square root symbol, but it can also be used for cube roots, fourth roots, etc. The number inside the radical is called the radicand, and the small number written above the radical (if present) indicates the type of root being taken (this is called the index).
Definition:
The square root symbol represents the square root, which is the number that, when multiplied by itself, gives the radicand.
A cube root is represented by cubert(a), which means the number that, when multiplied by itself three times, gives the radicand.
Examples:
sqrt(16) = 4 because 4 • 4 = 16.
cubert(27) = 3 because 3 • 3 • 3 = 27.
Key Points:
The index is usually not written for square roots, meaning sqrt(a) implies a square root (index of 2), but for cube roots and higher, the index is written as a small number above the radical (e.g., cubert(a)) for a cube root).
Radicals are used to represent non-integer roots, such as square roots and cube roots, and can be simplified using properties like the product and quotient properties of square roots.