1. Benchmark: H.1.1.a. Extend the properties of exponents to rational exponents. H.1.1.a.ii. Rewrite expressions involving radicals and rational exponents using the properties of exponents. Objectives:  find all the prime factors of a number  simplify radical expressions

2. Radicals  Because = 4 : 2 is a square root of 4  In the expression, the is the radical sign and 64 is the radicand.

3. Example1 Find the square root:

4. Practice1 Find the square root:

5. Perfect Squares List some perfect squares. 1 1= ____22 = ____33 = ____ 44 = _____ 55 = _____ 66 = ____ 77 = ____ 88 = _____ 99 = _____ 1010 = ______ 14 9 16 25 36 49 6481 100

6. The FANCY way to simplify a radical expression Simplify : Ugly Answer: ____________ 12.1244

7. The FANCY way to simplify a radical expression Simplify : Step 1: Find a perfect square that goes into 147.

8. The FANCY way to simplify a radical expression Simplify : Step 2: Split up the radical and simplify.

9. The EASY way to simplify a radical expression  Factoring is a way to find ALL the prime numbers that go into a number.  A prime number can only be divided by 1 and itself.

10. Example 2 Find all the prime factors of 300. 300 150 2 275 5 15 53

11. Practice 2 Find all the prime factors of 126. 126 63 2 321 3 7

12. The EASY way to simplify a radical expression  When simplifying a square root, the first step is to factor the number.  Only take 1 number from each pair outside of the radical.

13. Example 3: Use whiteboard to factor Simplify the following expression: 605 121 5 11

14. Example 3 Simplify the following expression:

15. Example 3 Simplify the following expression: DOUBLE CHECK!!

16. Practice 3 Simplify the following expression: 72 36 2 218 2 9 33

17. Practice 3 Simplify the following expression:

18. Practice 3 Simplify the following expression: DOUBLE CHECK!!

19. Example 4 Simplify the following expression: 75 15 5 35

20. Simplify the following expression: Example 4

21. Practice 4 Simplify the following expression: 90 45 2 59 3 3

22. Simplify the following expression: Practice 4

23. Example 5 Simplify the following expression: 49 7 7

24. Simplify the following expression: Example 5

25. Practice 5 Simplify the following expression: 8 4 2 22

26. Practice 5 Simplify the following expression:

27. Example 6 The formula can be used to find the size of a square sector where a is the area of the square and s is the length of a side. What is the length of the side of a square with an area of 729 sq. miles? 729 = a or s?

28. Whiteboards!!!

29. Find the square root:

32. Draw a factor tree for: 50 50 10 5 2 5

33. Simplify the following expression:

34. Draw a factor tree for: 63 63 9 7 3 3

35. Simplify the following expression: