Learning Objectives:

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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