Learning Objectives:

__Online Tutoring on Simplifying Radicals__

First, we will take a look at **simplifying radicals** that do not involve fractions. A **radical** is not simplified if the** radicand** or the number underneath the **radical** contains perfect **nth** **root** factors. So here's how we will accomplish **simplifying radicals.**

**1.** We are going to write the **prime factorization** of the **radicand.**

** 2. **Then we will circle the **nth root factors** which mean we will circle the equal factors in groups the same number as the **index.**

** 3.** The circled factors are the **perfect nth roots** that can be simplified, and the factors not circled will remain under the **radical.**

** 4.** Then once we do this we will **re-write **the** radical** in simplified form. Let us take a look at all types of **radical expressions**. All of these statements must be true in order for a **radical** to be in simplified form.

**1.** All possible **nth powered factors** have been removed from each **radical. **

**2.** No **radical** contains a fraction.

**3.** No denominator of a fraction contains a **radical.**

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**Hook Questions:**

*1. **How do you solve a square root?*

*2. **What is a radical in algebra?*

*3. **How do you multiply two square roots? *

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