Square Roots and

1. Section 0-9
Square Roots and Simplifying Radicals
Tuesday, September 20, 2011

2. Essential Question
How do you evaluate square roots and simplify radical
expressions?
Tuesday, September 20, 2011

3. Vocabulary
1. Product Property:
2. Quotient Property:
Tuesday, September 20, 2011

4. Vocabulary
1. Product Property: For two numbers a and b ≥ 0,
ab = ai b
2. Quotient Property:
Tuesday, September 20, 2011

5. Vocabulary
1. Product Property: For two numbers a and b ≥ 0,
ab = ai b
2. Quotient Property: For two numbers a and b ≥ 0,
a a
=
b b
Tuesday, September 20, 2011

6. Example 1
Simplify.
a. 54 b. 126
Tuesday, September 20, 2011

7. Example 1
Simplify.
a. 54 b. 126
9i7
Tuesday, September 20, 2011

8. Example 1
Simplify.
a. 54 b. 126
9i7
9i 7
Tuesday, September 20, 2011

9. Example 1
Simplify.
a. 54 b. 126
9i7
9i 7
3 7
Tuesday, September 20, 2011

10. Example 1
Simplify.
a. 54 b. 126
9i7 9i14
9i 7
3 7
Tuesday, September 20, 2011

11. Example 1
Simplify.
a. 54 b. 126
9i7 9i14
9i 7 9i 14
3 7
Tuesday, September 20, 2011

12. Example 1
Simplify.
a. 54 b. 126
9i7 9i14
9i 7 9i 14
3 7 3 14
Tuesday, September 20, 2011

13. Example 2
Simplify.
7 3 4
a. 80x y z b. 12 8 11
25a r t
Tuesday, September 20, 2011

14. Example 2
Simplify.
7 3 4
a. 80x y z b. 12 8 11
25a r t
6 2 4
16i5ix ixiy iyiz
Tuesday, September 20, 2011

15. Example 2
Simplify.
7 3 4
a. 80x y z b. 12 8 11
25a r t
6 2 4
16i5ix ixiy iyiz
3 2
4 x yz 5xy
Tuesday, September 20, 2011

16. Example 2
Simplify.
7 3 4
a. 80x y z b. 12 8 11
25a r t
6 2 4
16i5ix ixiy iyiz 12 8
25ia ir it it 10
3 2
4 x yz 5xy
Tuesday, September 20, 2011

17. Example 2
Simplify.
7 3 4
a. 80x y z b. 12 8 11
25a r t
6 2 4
16i5ix ixiy iyiz 12 8
25ia ir it it 10
3 2 6 4 5
4 x yz 5xy 5a r t t
Tuesday, September 20, 2011

18. Example 3
Simplify.
25 81
a. b.
49 16
Tuesday, September 20, 2011

19. Example 3
Simplify.
25 81
a. b.
49 16
25
49
Tuesday, September 20, 2011

20. Example 3
Simplify.
25 81
a. b.
49 16
25
49
5
7
Tuesday, September 20, 2011

21. Example 3
Simplify.
25 81
a. b.
49 16
25 81
49 16
5
7
Tuesday, September 20, 2011

22. Example 3
Simplify.
25 81
a. b.
49 16
25 81
49 16
5 9
7 4
Tuesday, September 20, 2011

23. Example 4
Simplify.
7 9
a. b.
5 12
Tuesday, September 20, 2011

24. Example 4
Simplify.
7 9
a. b.
5 12
7 5
i
5 5
Tuesday, September 20, 2011

25. Example 4
Simplify.
7 9
a. b.
5 12
7 5
i
5 5
7 5
5
Tuesday, September 20, 2011

26. Example 4
Simplify.
7 9
a. b.
5 12
7 5 9 12
i i
5 5 12 12
7 5
5
Tuesday, September 20, 2011

27. Example 4
Simplify.
7 9
a. b.
5 12
7 5 9 12
i i
5 5 12 12
7 5 9 12
5 12
Tuesday, September 20, 2011

28. Example 4
Simplify.
7 9 9 4i3
a. b.
5 12 12
7 5 9 12
i i
5 5 12 12
7 5 9 12
5 12
Tuesday, September 20, 2011

29. Example 4
Simplify.
7 9 9 4i3
a. b.
5 12 12
7 5 9 12 18 3
i i
5 5 12 12 12
7 5 9 12
5 12
Tuesday, September 20, 2011

30. Example 4
Simplify.
7 9 9 4i3
a. b.
5 12 12
7 5 9 12 18 3
i i
5 5 12 12 12
7 5 9 12 3 3
5 12 2
Tuesday, September 20, 2011

31. Example 5
Simplify.
4
a.
1− 7
Tuesday, September 20, 2011

32. Example 5
Simplify.
1+ 7 4
a. i
1− 7 1+ 7
Tuesday, September 20, 2011

33. Example 5
Simplify.
1+ 7 4
a. i
1− 7 1+ 7
4(1+ 7)
(1− 7)(1+ 7)
Tuesday, September 20, 2011

34. Example 5
Simplify.
1+ 7 4
a. i
1− 7 1+ 7
4(1+ 7)
(1− 7)(1+ 7)
4+ 4 7
1− 7 + 7 − 7
Tuesday, September 20, 2011

35. Example 5
Simplify.
1+ 7 4
a. i
1− 7 1+ 7 4+ 4 7
4(1+ 7) −6
(1− 7)(1+ 7)
4+ 4 7
1− 7 + 7 − 7
Tuesday, September 20, 2011

36. Example 5
Simplify.
1+ 7 4
a. i
1− 7 1+ 7 4+ 4 7
4(1+ 7) −6
(1− 7)(1+ 7) 2+ 2 7
4+ 4 7 −3
1− 7 + 7 − 7
Tuesday, September 20, 2011

37. Example 5
Simplify.
5
b.
6+ 8
Tuesday, September 20, 2011

38. Example 5
Simplify.
5 6− 8
b. i
6+ 8 6− 8
Tuesday, September 20, 2011

39. Example 5
Simplify.
5 6− 8
b. i
6+ 8 6− 8
5(6 − 8)
(6 + 8)(6 − 8)
Tuesday, September 20, 2011

40. Example 5
Simplify.
5 6− 8
b. i
6+ 8 6− 8
5(6 − 8)
(6 + 8)(6 − 8)
30 − 5 8
36 + 6 8 − 6 8 − 8
Tuesday, September 20, 2011

41. Example 5
Simplify.
5 6− 8 30 − 5 4i2
b. i
6+ 8 6− 8 36 − 8
5(6 − 8)
(6 + 8)(6 − 8)
30 − 5 8
36 + 6 8 − 6 8 − 8
Tuesday, September 20, 2011

42. Example 5
Simplify.
5 6− 8 30 − 5 4i2
b. i
6+ 8 6− 8 36 − 8
5(6 − 8) 30 − 10 2
(6 + 8)(6 − 8) 28
30 − 5 8
36 + 6 8 − 6 8 − 8
Tuesday, September 20, 2011

43. Example 5
Simplify.
5 6− 8 30 − 5 4i2
b. i
6+ 8 6− 8 36 − 8
5(6 − 8) 30 − 10 2
(6 + 8)(6 − 8) 28
30 − 5 8 15 − 5 2
36 + 6 8 − 6 8 − 8 14
Tuesday, September 20, 2011

44. Problem Set
Tuesday, September 20, 2011

45. Problem Set
p. P20 #1-20 all
“Hold yourself responsible for a higher standard than anyone else
expects of you. Never excuse yourself.” - Henry Ward Beecher
Tuesday, September 20, 2011