Transcript 10.3 Multiplying, Dividing, and Simplifying Radicals 1. Multiply radical expressions. 2. Divide radical expressions. 3.

10.3
Multiplying, Dividing, and Simplifying
Radicals
1. Multiply radical expressions.
2. Divide radical expressions.
3. Use the product rule to simplify radical expressions.
4  25  2  5  10
100  10
Product Rule for Radicals
If both n a and n b are real numbers, then
n
a  n b  n a  b.
The index (root) must be the same!
Multiply:
3
3  12

36  6
5 7

35
3a  5b

15ab
xy  7x

3
3
2
7x y
16
25
4

5
16
25
4

5
Quotient Rule for Radicals
If both n a and n b are real numbers, then
n
a na

, where b  0.
n
b
b
The index (root) must be the same!
Divide:
49
64
15
81
7

8

15
9
Divide:
243

3
21

3
243

3
21 
3
81  9
7
Simplify radicals:
Look for the largest perfect square that divides into the radicand evenly.
1
4
9
16
25
36
49
64
81
100
20 
4  5
75 
25  3 
60 
4  15 
48 
16  3 
4 
5 2 5
25 
3 5 3
4
15 2 15
16 
3 4 3
Simplify radicals:
245
1
4
9
16
25
36
49
64
81
100
Create a factor tower.
9 
33  3
20  2 5
20 
5
2 10
10
2 2 20
 2 5
Divide by prime numbers!
2, 3, 5, 7, 11, …
225
60
 2 15
60
5
3 15
15
22 30
30
22 2 60

2235
 2 35
 2 15
48  4 3
3
26
6
22 12
12
222 24
24
2222 48
48  2  2  2  2  3
 22 3
 4 3
Simplify radicals:
245 
1
4
9
16
25
36
49
64
81
100
577
 7 5
7
7 49
49
5 245
Simplify radicals:
300 
1
4
9
16
25
36
49
64
81
100
100  3  10 3
5
5 25
3 75
2 150
2
300
25 3
10 3
Simplify radicals:
52
1
4
9
16
25
36
49
64
81
100

13
2 26
2 52
4  13
 2 13
2 13
Simplify radicals:
108 
1
4
9
16
25
36
49
64
81
100
3
3 9
3 27
2 54
2 108
36  3
23 3
6 3
 6 3
Simplify.
486
a) 6 9
b) 3 54
c) 9 6
d) 18 27
Copyright © 2011 Pearson Education, Inc.
Slide 10- 16
Simplify.
486
a) 6 9
b) 3 54
c) 9 6
d) 18 27
Copyright © 2011 Pearson Education, Inc.
Slide 10- 17
Simplify radicals:
x
3

x 
5
x  x  x  x
x
x  x  x  x  x x  x
 x
1 R1
2 3
Think…
2 R1
2 5
2
x
x
Simplify radicals:
x
9
 x
4
x
Think:
4 R1
2 9
Simplify:
75 x 7 y 3 
75 
25∙3
x
7
3 R1
2 7
 5x 3y 3
33xxy

y
3
1 R1
2 3
Simplify:
48a b c 
3
7
4
48 
16∙3
a 
3
1 R1
2 3
 4a
ab3c323
3ab
3
aab
b 
7
3 R1
2 7
c
4
2 R0
2 4
Simplify radicals:
3
1
8
27
64
125
216
343
250 
5
5 25
5 125
2 250
3
125  2
 5
53 2
3
2
Simplify radicals:
3
1
8
27
64
125
216
343
243 
3
3 9
3 27
3 81
3 243
3
27  9
 3
33 9
3
9
Simplify:
3
24 x 7 y 2 z 5
3
24 
8∙3
3
x7 
2R1
3 7
y2 
3
0R 2
3 2
22 2
33333
 2x 2z
3
x
3
xy
z
xy
3
3
z5
1R 2
3 5
Simplify:
6 15c  2 10c
2
1
4
9
16
25
36
49
64
81
100
5
 12 150c 7
25∙6
 12  5c
3
 60c
6c
3
6
6c
Simplify:
1
4
9
16
25
36
49
64
81
100
9
54 240r s
6 4
9 5r s
10
9
54

9
240r s
6 4
5r s
 6 48r s
3
6
16∙3
 6  4rs
r 33
r3r
3
 24rs
3
3r
10
Simplify.
3m2 9m3
a) 3m 3m
b) 3m2 3m
c)
6
27m
d) 3m2 3m3
Copyright © 2011 Pearson Education, Inc.
Slide 10- 27
Simplify.
3m2 9m3
a) 3m 3m
b) 3m2 3m
c)
6
27m
d) 3m2 3m3
Copyright © 2011 Pearson Education, Inc.
Slide 10- 28