Properties Of Radicals, Simplifying Radicals, Rationalizing Operations Worksheet - Section A-7 Page 5
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1
2
3
4
5
6
7
8
9A-61
A-7 Radicals
3
3
1/2
1/3
(D)
27
[(3
)
]
3
1/6
3/6
1/2
(3
)
3
3
3
Express radicals in simplified form.
M A T C H E D P R O B L E M
3
4
3 4
9
3
5
2
3
3
5
3
6
3
(A)
18x
y
z
(B)
27a
b
3a
b
(C)
8x
y
(D)
4
Sums and Differences
Algebraic expressions involving radicals often can be simplified by adding and
subtracting terms that contain exactly the same radical expressions. We proceed
in essentially the same way as we do when we combine like terms in polynomi-
als. The distributive property of real numbers plays a central role in this process.
E X A M P L E
Combining Like Terms
4
Combine as many terms as possible.
(5
4) 3
(A)
5 3
4 3
9 3
3
3
3
3
2
2
2
2
(2
7)
xy
(B)
2
xy
7
xy
5
xy
3
3
3
3
3 xy
4 xy
2
xy
7
xy
(C)
3 xy
2
xy
4 xy
7
xy
3
7 xy
9
xy
Combine as many terms as possible.
M A T C H E D P R O B L E M
4
5
5
2
3
2
3
(A)
6 2
2 2
(B)
3
2x
y
8
2x
y
3
3
2
2
(C)
5
mn
3 mn
2
mn
7 mn
Products
We will now consider several types of special products that involve radicals. The
distributive property of real numbers plays a central role in our approach to these
problems.
E X A M P L E
Multiplication with Radical Forms
5
Multiply and simplify.
(A)
2( 10
3)
2 10
2 3
20
3 2
2 5
3 2
(B)
( 2
3)( 2
5)
2 2
3 2
5 2
15
2
2 2
15
2 2
13
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