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Radical Expressions MAT/117 Version 9
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Copyright © 2013 by University of Phoenix. All rights reserved.
University of Phoenix Material
Introduction to Radical Expressions The goal of this week is to introduce the algebraic concept of radical expressions. Radical expressions
are algebraic expressions containing a radical, such as √ .
Radical Expressions
In Cognitive Tutor, you will learn that the root of a number is written as √
and it means “What number
raised to n power results in a?” or put another way, ( ) .
Examples:
A. √ means ( ) Example A is read as “the square root of 36” and the answer is 6 because 6
2 = 36.
B. √
means ( ) Example B is read as “the cube root of 27” and the answer 3 because 3
3 = 27.
C. √
means ( ) Finally, Example C is read as “the fifth root of 32” and the answer is 2 because 2
5 = 32.
These are examples of perfect roots because the roots are integers (see Phoenix Math: Topic 21).
There will be many instances when the root of a number is not an integer. For example, √ has no integer root because there is no integer that you can square to get a result of 12. However, these types of roots can be simplified in radical form by using the product rule of radicals that is stated below.
√
√
√
The basic idea consists on rewriting the radicand (expression inside of the radical) as a product of two integers, but one of the integers is a perfect root. Here is an example:
√ √ √ √ √ Understanding how to find nonperfect roots in radical form is necessary to simplify the process of performing basic operations with radical expressions, which you will learn in Cognitive Tutor.
Fractional Exponents
The root of a number can also be written using fractional exponents instead of using the radical symbols. Here is how:
Radical Expressions MAT/117 Version 9
2
Copyright © 2013 by University of Phoenix. All rights reserved.
√
( )
and √
( )
Examples:
√
√
Writing radical expressions with fractional exponents provides an alternative method for performing operations with radicals using the exponent rules you learned in the Algebra 1a course, particularly when operations with radicals seems impossible. For example, multiplying two radical expressions with different indexes:
√ √
( )
( )
( )
√
