11-3 simplifying radical expressions standard 2.0 one property
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11-3Simplifying Radical Expressions
Standard 2.0One Property
CA Standard 2.0
Understand and use the operation of taking a root.
Product Properties for Radicals
For any nonnegative real numbers x and y.
yxxy a.
b.
xxx
Using the Product Properties
1.
2.
3.
4.
1.
2.
3.
4.
125
767
449
67
1243
60
25511 555555
Rules for Radical Expressions
a. Simplify the radicand first
b. When odd powers occur, express the power as the product of the largest even power and your exponential base.
c. Simplify your perfect squares.
#5 Simplify
32
2 16 4
24
#6 Simplify
45
5 9 3
53
#7 Simplify
96
16 6
64
2 3 6
#8 Simplify
216
2 108
66
2 54
6 9
#9 Simplify
All even powers are perfect squares.
8y
21
8y
4y
#10 Simplify
14)( yx
21
14yx
7yx
#11 Simplify
x60
x154
x152
#12 Simplify
240y
2104 y
102y
#13 Simplify
Express odd powers as the product of the largest even power and your exponential base.
15a
aa 21
14
aa7
aa14
#14 Simplify
25m
mm 21
24
mm12
mm24
#15 Simplify
7147 2 xx
)12(7 2 xx
2)1(7 x
17 x
2)1(7 x
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