Multiplying and Simplifying Radical Expressions
Note that 
= 2. 5 – 10. Also 
= 
= 10.Likewise,
![\sqrt[3]{27} \sqrt[3]{8}](https://mymathangels.com/wp-content/ql-cache/quicklatex.com-b87348da75a415a4af2013beeff039da_l3.png "Rendered by QuickLaTeX.com")
= 3.2 = 6 and ![\sqrt[3]{27.8} = \sqrt[3]{216}](https://mymathangels.com/wp-content/ql-cache/quicklatex.com-d467f4c6fe4ba5b54dc878c11149699f_l3.png "Rendered by QuickLaTeX.com")
= 6.
SIMPLIFYING kth ROOTS
To simplify a radical expression by factoring:
a. Look for the largest factors of the radicand that are perfect kth
powers (where k is the index).
b. Then take the kth root of the resulting factors.
c. A radical expression, with index k, is simplified when its radicand
has no factors that are perfect kth powers.
In many situations, expressions under radicals never represent
negative numbers. In such cases, absolute-value notation is not
necessary. For this reason, we will henceforth assume that all
expressions under radicals are nonnegative.