SIMPLIFYING RADICALS Simplest form Similar radicals 2nd level ? Simplifying powers Factors?of the radicand Fractional radicand WE SAY THAT A SQUARE ROOT RADICAL?is?simplified, or in its?simplest form, when the?radicand?has no?square?factors. A radical is also in simplest form when the radicand isnot a fraction. Example 1.???33, for example, has no square factors. ?Its factors are 3??11, neither of which is a square number. ?Therefore,??is in its simplest form. Example 2.???18 has the square factor 9. ?18 = 9??2. ?Therefore,??is not in its simplest form.? To put a radical in its simplest form, we make use of this theorem: The square root of a product? is equal to the product of the square roots? of each factor. (We will prove that when we come to?rational exponents, Lesson 29.

# Simplifying Different Types of Radical Expressions

SIMPLIFYING RADICALS Simplest form Similar radicals 2nd level ? Simplifying powers Factors?of the radicand Fractional radicand WE SAY THAT A SQUARE ROOT RADICAL?is?simplified, or in its?simplest form, when the?radicand?has no?square?factors. A radical is also in simplest form when the radicand isnot a fraction. Example 1.???33, for example, has no square factors. ?Its factors are 3??11, neither of which is a square number. ?Therefore,??is in its simplest form. Example 2.???18 has the square factor 9. ?18 = 9??2. ?Therefore,??is not in its simplest form.? To put a radical in its simplest form, we make use of this theorem: The square root of a product? is equal to the product of the square roots? of each factor. (We will prove that when we come to?rational exponents, Lesson 29.

## Need Help?

We hope your visit has been a productive one. If you're having any problems, or would like to give some feedback, we'd love to hear from you.

For general help, questions, and suggestions, try our dedicated support forums.

If you need to contact the Course-Notes.Org web experience team, please use our contact form.

## Need Notes?

While we strive to provide the most comprehensive notes for as many high school textbooks as possible, there are certainly going to be some that we miss. Drop us a note and let us know which textbooks you need. Be sure to include which edition of the textbook you are using! If we see enough demand, we'll do whatever we can to get those notes up on the site for you!