A radical is a root of a number or expression, such as . Definition: if and only if . The word radical can also be used to indicate the symbol indicating root, such as . When used as an adjective, the word radical means 'having to do with the taking of a root'. For example, a radical equation is an equation containing a variable inside a radical, or the root of a variable.
A radical with no number to the left is used to represent a square root. For example, means the square root of 7. If an integer appears to the left of the radical sign, it means an n^{th} root. The expression means the cube root of 4. The expression means the 4^{th} root of 7.
A radicand is the number or expression inside a radical: . For example: in , 3 is the radicand; in , x + 2 is the radicand; and in , t is the radicand.
A radical is the same as a exponent of a unit fraction. For example, . In general, . To convert a radical to an exponent, make the radicand the base, and the number to the left of the radical the denominator of the unit fraction in the exponent. 

A radical can be simplified if it contains a factor raised to the power of the radical. For example, Since , and , then . The steps to simplify a radical are:
Equation to simplify  Prime factorization  Divided into groups  Groups pulled out 

. Note that there are no groups of 3.  . This radical can not be simplified.  
Table 2: Examples of simplifying radicals 
#  A  B  C  D 
E  F  G  H  I 
J  K  L  M  N 
O  P  Q  R  S 
T  U  V  W  X 
Y  Z 
All Math Words Encyclopedia is a service of
Life is a Story Problem LLC.
Copyright © 20052011 Life is a Story Problem LLC. All rights reserved.
This work is licensed under a Creative Commons AttributionNoncommercialShare Alike 3.0 License