1. Standard MCC8EEb Simplify, Add, Subtract, Multiply, and Divide Radical Expressions

2. Sometimes numbers under the radical sign √, disguise themselves. First---ALWAYS check to see if they are PERFECT SQUARES—if so, take them out of the radical sign. First---ALWAYS check to see if they are PERFECT SQUARES—if so, take them out of the radical sign. Second—check their factors—in other words, what number times what number equals it. Second—check their factors—in other words, what number times what number equals it. Example----√8 is not perfect BUT you can break it into 4 x 2. AND….4 is PERFECT Example----√8 is not perfect BUT you can break it into 4 x 2. AND….4 is PERFECT SOOOOOOOOOOOOOOOOOOOOO SOOOOOOOOOOOOOOOOOOOOO

3. Break it down! √8 = √4 x √2 √8 = √4 x √2 Then-----√4 becomes a whole number 2 Then-----√4 becomes a whole number 2 We write 2 √2. We write 2 √2. Ta-dah!!!!! This is your answer! Ta-dah!!!!! This is your answer!

4. Another one √12 = ? X ? where one of the numbers is a perfect square √12 = ? X ? where one of the numbers is a perfect square That’s right---4 x 3 That’s right---4 x 3 So, √4 x √3 = √12 So, √4 x √3 = √12 Write √4 as 2 and leave √3 alone Write √4 as 2 and leave √3 alone

5. And the answer is….. 2 √3 2 √3

6. Your turn to practice √18 √18 √24 √24 √28 √28 √40 √40

7. OK—now just a bit harder…. Sometimes you miss the largest square. If you do, don’t panic--- Sometimes you miss the largest square. If you do, don’t panic--- √72----most people say 9 x 8 √72----most people say 9 x 8 √9 x √8 changes to 3 √8 √9 x √8 changes to 3 √8 BUT…….. BUT……..

8. Watch carefully √8 breaks into 4 x 2 √8 breaks into 4 x 2 3 √8 continues to break down 3 √8 continues to break down Change √8 to 2 √2----take the outside 2 and multiply it by the outside 3 to get 6. Change √8 to 2 √2----take the outside 2 and multiply it by the outside 3 to get 6. Final answer-----6 √2 Final answer-----6 √2

9. Always check your answer….. 6 √2 means 6 x 6 = 36 6 √2 means 6 x 6 = 36 36 x 2 = 72----the number we started with 36 x 2 = 72----the number we started with You try: You try: 2√8 2√8 4 √12 4 √12 3 √18 3 √18

10. The answers are…. 2√8= 4√2 2√8= 4√2 4 √12=16√3 4 √12=16√3 3 √18= 9√2 3 √18= 9√2

11. Now, there is more to this… Multiplying radicals is easy—just put together what goes together and always check to see if you can reduce. Multiplying radicals is easy—just put together what goes together and always check to see if you can reduce. √8 x √3 = √24 √8 x √3 = √24 √24 = 4 x 6 √24 = 4 x 6 Change 4 into 2—leave the 6 in the crazy house Change 4 into 2—leave the 6 in the crazy house 2 √6 2 √6

12. More examples