Overview

Simplifying

Simplifying radicals is important when an exact value is required or to make a complex variable expression easier to manipulate. The first step is to determine what power is important by looking at the degree of the root. If the expression contains a cube root, then perfect cubes will be needed. Likewise, if the expression contains an nth root, then numbers or variables to the nth power will be needed. The Product Property of Roots is also needed and will be explained in greater detail later in this book.

Example 1 Simplify simplify_1 .

Step 1. Determine the degree of the root.

This expression is a square root, so the degree is 2.

Step 2. Find a perfect square factor under the radical.

simplify_2

Step 3. Use the Product Property of Roots to simplify.

simplify_3