Transcript 10.4 Adding, Subtracting, and Multiplying Radical Expressions 1. Add or subtract like radicals. 2.

10.4
Adding, Subtracting, and Multiplying
Radical Expressions
1. Add or subtract like radicals.
2. Use the distributive property in expressions containing
radicals.
3. Simplify radical expressions that contain mixed
operations.
Simplify.
6
1)
5t 3s 10
9
3
5a 4b 2ab
4
10
25t s
2)
3)
20
50a b
3
81m n
3 3
3mn
3mn
Adding Radical Expressions
2x  5 x  7 x
2 3 5 3  7 3
Like radicals: Radical expressions with identical
radicands and indices (roots).
Adding Like Radicals
Add or subtract the coefficients and leave the
radical parts the same.
Add:
3 25 2
 2 2
3y 3 4 8y  9y 3 4 8y  6y 3 4 8y
Add:
3 24  54
4∙6
9∙6
32 6
6 6
3 6
9 6
Add:
27 x  75 x
9∙3
25∙3
3 3x  5 3x
8 3x
Add:
4 98 y 5  6 128 y 5
49∙2
64∙2
2
4  7y 2 2y  6  8y 2y
28y
2
2

48
y
2y
2y
 20y
2
2y
Add:
6y
4
6y  3y
18y
81y 5  2y 4 16 y 6
4
24
y
y
 2y  2y

24
4y
y
4
2
y2
Simplify. 2 12  5 27  48  2 3
a) 9  3
b) 17 3
c) 71 3
d) 25 3
Copyright © 2011 Pearson Education, Inc.
Slide 10- 9
Simplify. 2 12  5 27  48  2 3
a) 9  3
b) 17 3
c) 71 3
d) 25 3
Copyright © 2011 Pearson Education, Inc.
Slide 10- 10
Simplify:
23 x  4   6 x  8
Distributive Property
2 32  6 
64  12
82 3
If the indexes are
the same, multiply
the radicands.
Simplify:
3a  25a  7
Foil
15a 2  21a  10a  14
15a 2  11a  14
7 
3  5  2 
7 5  7 2  15 
Multiply coefficients.
Multiply radicals.
6
Simplify:
Rewrite and Foil!


7  3
2
7  3 7  3
49  3 7  3 7  9
76 79
16  6 7
5 x  32
5 x  35 x  3
25 x 2  15 x  15 x  9
25 x 2  30 x  9
Multiply coefficients.
Multiply radicals.
Simplify:
Conjugates

2x  52x  5
4 x 2  10 x  10 x  25
4 x 2  25
3  2 3  2
92 32 34
34
1
To multiply radicals, the index must be the
same.
If the index is the same, multiply the coefficients
together and multiply the radicands together.
To add radicals, the radicals must be the same
(same index and same radicand).
Add the coefficients together and keep the same
radical.
Simplify:
7 5  3 14 
35  3 98
49∙2
35  3  7 2
35  21 2
Simplify:
5 
a 2  a 
10  5 a  2 a  a2
10  3 a  a
Simplify:

3
3
9  53 9  2
81  2 3 9  5 3 9  10
27∙3
3
33 3  3 9  10
Simplify:
3  2 5 
2
3  2 5 3  2 5 
9  6 5  6 5  4 25
9  12 5  4  5
9  12 5  20
29  12 5
Multiply.  3 2  3 2  5 3 
a) 9 15 6  3 2
b) 6  3 2 15 3 15 6
c) 5 14 6 15 3
d) 25 3
Copyright © 2011 Pearson Education, Inc.
Slide 10- 20
Multiply.  3 2  3 2  5 3 
a) 9 15 6  3 2
b) 6  3 2 15 3 15 6
c) 5 14 6 15 3
d) 25 3
Copyright © 2011 Pearson Education, Inc.
Slide 10- 21