1. Warm Up Simplify using only positive exponents. 1.7n 2 3n 5 2.(4y 6 ) 3 Solve for the value of x. 3.

2. Answers Simplify using only positive exponents. 1.7n 2 3n 5 = 21n 7 2.(4y 6 ) 3 = 64y 18 Solve for the value of x. 3. x = 3

4. Essential Question How can properties of exponents be used to write radical expressions in useful equivalent forms?

5. What is a radical? We are familiar with taking square roots and even taking cubed roots, but you may not be as familiar with the elements of a radical.

6. The index in a radical tells you how many times you have to multiply the root times itself to get the radicand. Example: 81 is the radicand, 3 is the root, and the index is 4. You have to multiply 3 by itself 4 times to get the radicand. 3333 = 81

7. Evaluating Radicals  Radicand:  Index:  Root: because  Radicand:  Index:  Root: because

8. Evaluating Radicals with the Calculator For some of the more complex problems, you can use a calculator to help Step 1: Type in the index Step 2: Press MATH Step 3: Choose 5 Step 4: Type in the radicand

9. Simplifying Radicals Investigation Now you will have a chance to practice some on your own. Complete the three examples on the bottom of the page. Then move to the next side and read the introduction carefully. Your goal is to come up with methods and shortcuts to simplify the radicals. Resource Manager: Ensure everyone is on the right page Time Keeper: 10 minutes Reader/Recorder: Read each question and the introduction Spy Monitor: Check in with other groups or the key

10. Simplifying Radicals 1)Find the Prime Factorization of the radicand 2)Any sets of “n” numbers (n=index) have one representative multiplied outside 3)Any remaining numbers no in a set are multiplied inside.

11. Examples In your groups, complete the remaining problems

12. Multiplying Radicals When written in radical form, it’s only possible to write two multiplied radicals as one if the index is the same. 1)Multiply the coefficients 2)Multiply the radicands 3)Simplify!

13. Examples In your groups, complete the remaining problems

14. Adding & Subtracting Radicals You can only add or subtract radicals that contain the same index and radicand. Just like you don’t change the variable expression, you won’t change the radical expression. Only add and subtract the coefficients. ALWAYS SIMPLFY THE RADICAL FIRST!

15. Examples In your groups, complete the remaining problems