TUTORIALS:
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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 a1/n is defined, then
the expression
is called a
radical, and
![](./articles_imgs/916/radica3.gif)
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 “square roots†and “cube roots,â€
respectively, whereas the expression
is “the nth root of a.†The index 2 is usually
omitted. We write
rather than
. Remember that
is simply another
notation for a1/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.
![](./articles_imgs/916/radica7.gif)
Solution
![](./articles_imgs/916/radica8.gif)
![](./articles_imgs/916/radica9.gif)
![](./articles_imgs/916/radica10.gif)
We can write either the root or the power first.
![](./articles_imgs/916/radica12.gif)
Example 2
Simplifying radical expressions
Simplify.
![](./articles_imgs/916/radica13.gif)
Solution
![](./articles_imgs/916/radica14.gif)
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