Properties Of Radicals, Simplifying Radicals, Rationalizing Operations Worksheet - Section A-7 Page 7
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1
2
3
4
5
6
7
8
9A-63
A-7 Radicals
3
3
3
3
3
2
2
2
2
2
2
2
2 3
a
b
2a
2a
2a
3
b
18a
b
3
(B)
3
3
3
3
3
3
2
2
2
2
3
b
3b
3b
3b
3
b
3b
(C) The special product in equation (1) suggests that if we multiply the denom-
inator
3 x
2 y
by
3 x
2 y
, we will obtain the difference of two
squares and the denominator will be rationalized.
x
y
( x
y)(3 x
2 y)
3 x
2 y
(3 x
2
y)(3 x
2 y)
2
2
3 x
2 xy
3 xy
2 y
2
2
(3 x)
(2 y)
3x
5 xy
2y
9x
4y
(D) The special product in equation (3) suggests that if we multiply the denom-
3
3
3
2
2
inator
m
2
by
(
m)
2
m
2
, we will obtain the sum of two cubes
and the denominator will be rationalized.
3
3
2
2
1
1[(
m)
2
m
2
]
3
3
3
3
2
2
m
2
(
m
2)[(
m)
2
m
2
]
3
3
2
m
2
m
4
3
3
3
(
m)
2
3
3
2
m
2
m
4
m
8
Rationalize denominators.
M A T C H E D P R O B L E M
6
3
6
10x
x
2
1
(A)
(B)
(C)
(D)
3
3
2x
4x
2 x
3
1
y
A n s w e r s t o M a t c h e d P r o b l e m s
5
9
9
5
2
5
2
2
5
2
3
1/4
4/7
3
3
1/3
1. (A)
u
(B)
(6x
y
)
or
(
6x
y
)
(C)
1/
(3xy)
(D) (9u)
(E)
(2x)
(F) (x
y
)
3
1
3
2
2
2
2
2. (A) u
v
(B)
2 3
(C)
(
x
)/2
or
x
2
4
3
3
2
2
2
2
2
3. (A) 3x
yz
2xz
(B) 3a
b
b
3a
b
b
(C)
2x
y
(D)
2
5
3
2
3
2
4. (A)
8 2
(B)
5
2x
y
(C)
3
mn
4 mn
3
3
2
2
5. (A)
3 2
4 3
(B)
2 3
5
(C)
y
2 y
8
(D)
x
x
y
xy
y
3
3
2
3 2x
2x
x
6
1
y
y
2 3
2
6. (A)
(B)
5x
2x
(C)
(D)
x
4x
9
1
y
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