Radical Expression
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 expression is an expression that involves a radical symbol, which represents the root of a number or an expression. The most common type of radical expression involves the square root, but it can also involve other types of roots, such as cube roots, fourth roots, etc.
Definition:
A radical expression is any expression that contains a radical sign or a root. The general form of a radical expression is:
Where:
n rt(a) is the n-th root of a,
n is the index (which determines the type of root: square root if n = 2, cube root if n = 3, etc.),
a is the radicand (the number or expression inside the radical).
Common Types of Radical Expressions:
1. Square root (when n = 2):
sqrt(a) the square root of a
2. Cube root (when n = 3):
cubert(a) the cube root of a
3. Fourth root (when n = 4):
4 rt(a) the fourth root of a
Examples of Radical Expressions:
sqrt(16) (the square root of 16, which equals 4),
cubert(27) (the cube root of 27, which equals 3),
4 rt(81) (the fourth root of 81, which equals 3).
Simplifying Radical Expressions:
A radical expression can often be simplified by factoring the radicand into perfect powers. For example:
sqrt(50) can be simplified to sqrt(25 • 2) = 5sqrt(2).
Conclusion:
A radical expression is a mathematical expression that involves roots. The radical symbol allows for the representation of roots such as square roots, cube roots, and higher-order roots, and it plays a key role in many areas of algebra and number theory.