PROPERTIES OF RADICALS 9

1. PROPERTIES OF
RADICALS
10/5/20

2. ACTIVITY

3. WHAT IS THE SQUARE and CUBE ROOT
OF THE FOLLOWING!
1. 100
2.
3
8
3. 81
4.
3
216
5.
3
64
10
2
4
6
9

4. Let a and b real numbers,
variables or algebraic expression
such that the indicated roots are
real numbers, and let m and n be
positive integers.

5. EXAMPLE: PROPERTY
1.
𝑛
𝑎 𝑚 = ( 𝑛
𝑎) 𝑚
3
82 = (
3
8)2 = (2)2
= 4

6. EXAMPLES:
PROPERTY (Product Rule for Radicals)
2. 𝑛
𝑎 •
𝑛
𝑏 = (
𝑛
𝑎𝑏)
5 • 7 = 5 • 7 = 35
3
2 •
3
5 =
3
2 • 5 =
3
10

7. QUIZ!
IN YOUR NOTEBOOK
ANSWER PAGE 160
TRY IT 1 (a-d)

8. SIMPLIFIED FORM OF A SQUARE
ROOT RADICAL
12 4 • 3=
=4 • 3 𝟐 𝟑

9. EXAMPLES:
25𝑥2 • 3𝑥 =25𝑥2 • 3𝑥 =
5𝑥 3𝑥5𝑥 • 3𝑥 =
𝟕𝟓𝒙 𝟑

10. EXAMPLES:
9𝑎2 𝑏2 • 5𝑎 =9𝑎2 𝑏2 • 5𝑎 =
3𝑎𝑏 5𝑎3𝑎𝑏 • 5𝑎 =
𝟒𝟓𝒂 𝟑 𝒃 𝟐

11. EXAMPLES:
2𝑥 36𝑥4 • 2𝑥2𝑥 36𝑥4 • 2𝑥 =
12𝑥2
2𝑥2𝑥(6 𝑥
2
) • 2𝑥 =
𝟐𝒙 𝟕𝟐𝒙 𝟓

12. ASSIGNMENT!
IN YOUR NOTEBOOK
ANSWER PAGE 162
TRY IT 2 (a-f)

13. EXAMPLES: PROPERTY (Quotient Rule for Higher
Order Radicals)
3.
𝑛
𝑎
𝑛
𝑏
=
𝑛 𝑎
𝑏
, 𝑏 ≠ 0
4
27
4
9
= 4
3
4 27
9
=

14. EXAMPLES: PROPERTY (Quotient Rule for Higher
Order Radicals)
3.
𝑛
𝑎
𝑛
𝑏
=
𝑛 𝑎
𝑏
, 𝑏 ≠ 0
28𝑥3
7𝑥
= 2𝑥28𝑥3
7𝑥
= 4𝑥2 =

15. EXAMPLES: PROPERTY (Quotient Rule for Higher Order Radicals)
3.
𝑛
𝑎
𝑛
𝑏
=
𝑛 𝑎
𝑏
, 𝑏 ≠ 0
250𝑥8
5𝑥4
=
5𝑥2
2
250𝑥8
5𝑥4
=
25𝑥4 • 2 =50𝑥4 =

16. EXAMPLES: PROPERTY (Quotient Rule for Higher Order Radicals)
3.
𝑛
𝑎
𝑛
𝑏
=
𝑛 𝑎
𝑏
, 𝑏 ≠ 0
2𝑥312𝑥7
3𝑥
= 4𝑥6 =

17. EXAMPLES: PROPERTY (Quotient Rule for Higher Order Radicals)
3.
𝑛
𝑎
𝑛
𝑏
=
𝑛 𝑎
𝑏
, 𝑏 ≠ 0
3𝑥
𝑥
3
𝑥
=
3
𝑥
•
𝑥
𝑥
=

18. EXAMPLES:
10
45
4
5
10 = 24
1
2 = 4 =

19. ASSIGNMENT!
IN YOUR NOTEBOOK
ANSWER PAGE 164
TRY IT 3 (a-b)

20. EXAMPLE: PROPERTY
4.
𝑚 𝑛
𝑎 = ( 𝑚𝑛
𝑎)
3
10 =
6
10
3
7 =
6
7

21. EXAMPLE: PROPERTY
5. ( 𝑛
𝑎) 𝑛
= 𝑎
( 3)2
= 3(3)
2
2=

22. EXAMPLE: PROPERTY
6. For n even,
𝑛
𝑎 𝑛 = ⃓ 𝑎⃓
(−12)
2
= 12⃓ − 12⃓ =
6. For n odd,
𝑛
𝑎 𝑛 = 𝑎
3
(−12)3
= (−12)
3
3 = −12

23. ASSIGNMENT!
IN YOUR NOTEBOOK
ANSWER PAGE 165
TRY IT 4 (a-b)

24. ASSIGNMENT!
IN YOUR NOTEBOOK
ANSWER PAGE 166
PRACTICE and APPLICATION
I. A: 1-5
B: 21-25
II. # 31-35