SIMPLIFYING+RADICALS

 =__Simplyfing Radicals__ =

W E SAY THAT A SQUARE ROOT RADICAL is "simplified" when the __radicand__ has no __square__ factors. **__Example 1.__** 33, for example, has no square factors. Its factors are 3**·** 11, neither of which is a square number. Therefore, is simplified, or, as we say, in its simplest form.

__**Example 2.**__ 18 has the square factor 9. 18 = 9**·** 2. Therefore, is not in its simplest form.

Therefore, = = **·**  = 3.

**__Example 3.__** Simplify. 180 = 2**·** 90 =2**·** 2**·** 45 = 2**·** 2**·** 9**·** 5 = 2**·** 2**·** 3**·** 3 **·** 5 Therefore, = 2**·** 3 = 6.

Try some simplyfing problems.... a) = b)  = c) = d)  = e) = f)  = g) = h)  = Now try to reduce to lowest terms....

2 || = ||  ||   ||   ||   ||   || 3 || = ||   ||   ||   ||   ||   || 2 || = ||
 * a) || [[image:http://www.themathpage.com/alg/Alg_IMG/sq20U.gif width="29" height="21"]]
 * b) || [[image:http://www.themathpage.com/alg/Alg_IMG/sq72U.gif width="29" height="21"]]
 * c) || [[image:http://www.themathpage.com/alg/Alg_IMG/sq22U.gif width="29" height="21"]]

Practice Sites: [|Simplifying Radicals] [|Lesson Simplify Radicals]