# Radical Notation

Any expression involving an nth root can be written using radical notation. The
symbol
is called the
**radical symbol**.

**Radicals **

If n is a positive integer and a is a real number for which a^{1/n} is defined, then
the expression
is called a
**radical**, and

The number a is called the **radicand**. The number n is called the **index
**of the
radical. Radicals of index 2 and 3 are referred to as â€œsquare rootsâ€ and â€œcube roots,â€
respectively, whereas the expression
is â€œthe nth root of a.â€ The index 2 is usually
omitted. We write
rather than
. Remember that
is simply another
notation for a^{1/n}. So
is the positive nth root of a when n is even and a is positive,
whereas
is the real nth root of a when n is odd and a is any real number.
The expressions

are not real numbers because there are no even roots of negative numbers in the real
number system.

**Example 1**

**Changing notations **

Write each exponential expression using radical notation and each radical expression
using exponential notation. Assume the variables represent positive numbers.
Do not simplify.

**Solution **

We can write either the root or the power first.

**Example 2**

**Simplifying radical expressions **

Simplify.

**Solution **