**Multiplying and Simplifying Radical Expressions**

Note that = 2. 5 – 10. Also = = 10.Likewise,

= 3.2 = 6 and = 6.

**SIMPLIFYING ***k***th ROOTS**

To simplify a radical expression by factoring:

**a. **Look for the largest factors of the radicand that are perfect *k*th

powers (where *k *is the index).

**b. **Then take the *k*th root of the resulting factors.

**c. **A radical expression, with index *k*, is *simplified *when its radicand

has no factors that are perfect *k*th 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.