1. Warm up February 17, 2011 Simplifying the following radicals 1. 2. 3. 4. 5.6.

2. Lesson 8.3 Simplifying Radical Expressions (With Variables) SWBAT: Multiply and simplify radical expressions containing numbers and variables

3. Remember yesterday? So we talked about simplifying radicals that involved numbers. Today, we are going to use the same “get out of jail” idea, except now we are going to apply it to variables…

4. Consider this guy: If we talk guards and prisoners, how many guards are there? How many prisoners? How many try to bust out? How many make it? How many are left to rot? 2 3 2 1 1

5. The Great Escape…Part Deux… So here is how it goes down this time. Those 3 prisoners, still not very smart, see that there are only two guards and think, hey, two of us can charge the guards and get away. So two of the prisoners go charging at the guards…but, only one gets away. One gets caught and is never seen or heard from again. And the third guy, since he didn’t have a partner to charge the guards with, he’s left to rot in prison. So once again…don’t lead a life of crime!

6. So…which is really just… so it ends up like this… This guy gets away This guy gets caught and is never heard from again This guy didn’t have a partner and so is left in prison The guy that got away The guy left in prison As for the missing guy…he’s Dead, gone, went bye bye, won’t see him again, hasta la vista!

7. Here’s another example: Try this one. How many guards? 2 How many prisoners? 5 How many are going to try to bust out? 4 Why only 4? The 5 th guy doesn’t have a partner.

8. How many actually make it outside if 4 try to escape? 2 How many are left in prison? 1, he didn’t have a partner. So then the simplified form of is…

9. Another Example Simplify the following radical expression. How many guards? How many prisoners are going to try to escape? How many left inside to rot? How many make it out of the big house? What is the answer?

10. Step 1: Factor Inside like normal. Step 2: Circle any sets. Box any left alone. Step 3: Pull one from each set out front of the radical…make sure you KEEP the 2 out front as well!!!! Step 4: Multiply everything left underneath together. Step 5: Multiply everything out front together. What if there is a coefficient?

11. Step 1: Factor Inside like normal. Step 2: Circle any sets. Box any left alone. Step 3: Pull one from each set outside the radical. Step 4: Multiply everything left underneath together. Step 5: Multiply everything out front together.

12. Try these by yourself. They all follow the same steps. 1. 2. 3. 4.