1. Aim #3.4: How do we simplify and multiply radicals? What is a radical? So, means what numbers times itself has a product of 16? means “the nth root of a.” 4 and -4

2. Aim #3.4: How do we simplify and multiply radicals? means what number times itself has a product of 27? 3

3. Aim #3.4: How do we simplify and multiply radicals? EVEN roots CANNOT have a negative under the radical! Remember, all positive roots have the potential to be both positive and negative! How do we know which answer they want? Check the front!, the front of the radical sign is positive, so give the positive answer of 3., the front of the radical sign is negative, so give the negative answer of -5

4. Aim #3.4: How do we simplify and multiply radicals?

5. Simplifying Non-perfect Roots: So, what happens if I am asked to find the square root of a non-perfect radical? Well, we would simplify it as much as possible, or take out perfect factors and leave the remaining under the radical. HINT: a factor tree usually works out well for this. ****Radicals that cannot be simplified are called PRIME (because there is a PRIME number under the radical ) ******

6. Aim #3.4: How do we simplify and multiply radicals?

7. Multiplying Radicals Radicals are special sets of numbers, they only associate with other radicals. That being said, if you multiply two radicals together, you multiply the numbers underneath the radical, put the radical sign over the answer, then simplify.

8. Aim #3.4: How do we simplify and multiply radicals? Hey, what if I have numbers (coefficients) in front of the radicals? Well, we can multiply those too, they just stay outside the radical. Ex:

9. Summary: Answer in complete sentences. List three things you learned to do in this lesson. Pick two concepts from this section and explain how to solve. Create a problem involving one of the concepts and then explain in words how to solve. Then solve it.