A. Radicals in Simplest Form

The first warm-up skill for Lesson 1.2 is to recognize whether or not a radical is in its simplest form. A radical is already in simplest form when the radicand no longer has any perfect square factors greater than 1 (for square roots).

Example 1

This mixed radical is in simplest form because the radicand 3 only has itself and one as factors.

So, is in simplest form.

Example 2

This entire radical is in simplest form because the radicand has no perfect square factors.

Neither or can be evaluated as a whole number.

So, is in simplest form.

Example 3

 This entire radical is not in simplest form because the radicand's largest perfect square factor is 16.

This mixed radical is now in simplest form.

Click here for this lesson in video format.