OPERATIONS IN RADICALS 9

1. 10.21/23.20

2. 𝑎 𝑥 + 𝑏 𝑥 = (a + b) 𝑥

3. 𝑎 𝑥 + 𝑏 𝑥 = (a + b) 𝑥

4. 𝑎 𝑥 + 𝑏 𝑥 = (a + b) 𝑥

5. 𝑎 𝑥 − 𝑏 𝑥 = (a − b) 𝑥

6. 𝑎 𝑥 − 𝑏 𝑥 = (a − b) 𝑥

7. (5𝑎 𝑎 + 2𝑎 𝑎) + (4𝑏 𝑎 − 2𝑏 𝑎)

8. QUIZ!
IN YOUR NOTEBOOK
ANSWER PAGE 169
TRY IT 1 (A & B)

15. QUIZ!
IN YOUR NOTEBOOK
ANSWER PAGE 170
TRY IT 2 (A)

20. QUIZ!
IN YOUR NOTEBOOK
ANSWER PAGE 170
TRY IT 3 (A & B)
TRY IT 4

21. 10.26/28.20

22. 3 12

23. 𝑎 𝑎5

24. 6 3 • 4 15

25. 7 2 • 5 • 10

26. 4 2 • 5 8

27. QUIZ! IN YOUR
NOTEBOOK
ANSWER PAGE 176
TRY IT 1 (A & B)

28. 3
2 • 2

29. 3
2 • 3

30. QUIZ! IN YOUR
NOTEBOOK
ANSWER PAGE 177
TRY IT 2 (A & B)

31. 3𝑥( 12𝑥 + 4)

32. 3( 6 + 2 3)

33. 5(2 5 + 2 3)

34. 3
2𝑎(
3
12𝑎 −
3
2𝑎)

35. 3
3𝑏(2
3
9𝑏 − 4
3
𝑏2)

36. QUIZ! IN YOUR
NOTEBOOK
ANSWER PAGE 178
TRY IT 4 (A & B)

37. ( 2 + 3)( 2 − 4)
2 − 2 − 12

38. ( 2 + 2)( 2 − 3)
2 − 2 − 6

39. ( 3 + 3)( 3 − 4)
3 − 3 − 12

40. (2 5 + 7)(2 5 − 4)
4 5 + 6 5 − 28
20 + 6 5 − 28

41. (3 2 + 5)(3 2 − 5)
9 2 − 25
18 − 28

42. QUIZ! IN YOUR
NOTEBOOK
ANSWER PAGE 179
TRY IT 5 (A & B)

43. ( 2 + 5)2
( 2)2
+2 2 5 + ( 5)2
2 + 2 10 + 5

44. ( 3𝑎 + 𝑏 6𝑐)2
( 3𝑎)2+2𝑏 3𝑎 6𝑐 + (𝑏 6𝑐)2
3𝑎 + 2𝑏 18𝑎𝑐 + 6𝑏2
𝑐
3𝑎 + 2𝑏 9 • 2𝑎𝑐 + 6𝑏2
𝑐

45. QUIZ! IN YOUR
NOTEBOOK
ANSWER PAGE 180
TRY IT 6 (A)

46. ( 5 + 3)( 5 − 3)
5 − 9

47. ( 2 + 2)( 2 − 2)
2 − 4

48. ( 5 + 4)( 5 − 4)
5 − 16

49. (3 2 + 5)(3 2 − 5)
9(2) − 25

50. (5 2𝑎 + 6)(5 2𝑎 − 6)
25(2𝑎) − 36

51. QUIZ! IN YOUR
NOTEBOOK
ANSWER PAGE 180
TRY IT 7 (A)

52. 8 24
16 6
=
8
16
24
6
=
1
2
4
=
1
2
(2)

53. 32 5
4 5
=
32
4
5
5
= 8 1
= 8 (1)

54. 20 3
5 3
=
20
5
3
3
= 4 1
= 4 (1)

55. 4 8𝑥5
2 2𝑥2
=
4
2
8𝑥5
2𝑥2
= 2 4𝑥3
= 2 4𝑥2 • 𝑥

56. 9𝑥23
16𝑥5
3𝑥
3
2𝑥2
=
9𝑥2
3𝑥
3 16𝑥5
2𝑥2
= 3𝑥
3
8𝑥3 = 3𝑥(2𝑥)

57. QUIZ! IN YOUR
NOTEBOOK
ANSWER PAGE 181
TRY IT 8 (A & B)

58. RATIONALIZING THE
DENOMINATOR
Multiple the numerator and
denominator by an expression
that will give an nth root of an
nth power in the denominator.

59. 7
5

60. 𝑥3
3

61. 12 2
2 27
=
𝟏𝟐 𝟐
𝟐(𝟑) 𝟑

62. 20 46
5 23
=
𝟒(𝟐𝟑) 𝟐
𝟐𝟑

63. 3
2 + 1

64. 6 2 + 5
6 2 − 5

66. (8 12 + 4 27) ÷ 3

67. =
28 3
3
•
3
3
=
28 9
3
=
28(3)
3
=
84
3

68. =
𝟑 𝟏𝟒 + 𝟒 𝟑𝟓
𝟕
•
𝟕
𝟕
=
𝟑 𝟏𝟒 • 𝟕 + 𝟒 𝟑𝟓 • 𝟕
𝟕
(𝟑 𝟏𝟒 + 𝟒 𝟑𝟓) ÷ 𝟕

70. QUIZ! IN YOUR
NOTEBOOK
ANSWER PAGE 183
TRY IT 10 (A)

71. QUIZ! IN YOUR
NOTEBOOK
ANSWER PAGE 184
TRY IT 11 (A)

72. ASSIGNMENT!