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
