Name
LESSON
8-6
Date
Class
Reteach
Radical Expressions and Rational Exponents
Use Properties of n th Roots to simplify radical expressions.
n n n
a 兹b
Product Property: 兹ab 兹
兹81x 8.
4
Simplify:
兹3 4 x 4 x 4
4 4 4 兹3 4 兹x 4 兹x 4
4
Factor into perfect fourth roots.
Use the Product Property.
3xx
3x 2
n 4 4 Think: 兹a n a, so 兹3 4 3 and 兹x 4 x .
n a
a
___
Quotient Property: n __ 兹
n b 兹
b
Always rationalize the denominator
9
3 __
x
when an expression contains a radical
Simplify:
.
2
in the denominator.
3 x9
兹
____
Use the Quotient Property.
3 兹2
3
Simplify the numerator. Think:
x
___
3 3 3 3 3 兹x 9 兹x 3 兹x 3 兹x 3 x x x.
兹2 3 3 3
2 兹
2
___
___
x 兹
___
Rationalize the denominator.
3 3 3 兹2 兹2 兹2
2
3 3
x 兹2
______
Use the Product Property.
3 兹2 3
3 3 x 兹4
_____
Simplify.
2
兹
兹
Simplify each expression.
3 3 8
4
1. 兹x 兹x
兹x 8 x 4
2.
8
x
__
6
兹
4
3.
4
3 3 6
兹125 兹x
4 兹6
x4
64
____
2x 10
3 3 5. 兹2x 兹4x 2
2
___
x
5x 2
6
兹
5
x 兹216
________
2 4
4.
3
x8
兹
____
3
兹125x 6
2x
2
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c08-6_rt.indd 46
46
6.
兹625x 8
4
5x 2
Holt Algebra 2
12/28/05 3:33:18 PM
Process Black
Name
Date
Class
Reteach
LESSON
8-6
Radical Expressions and Rational Exponents (continued)
The n th root of a number can be represented using a rational, or fractional,
1
__
n
exponent: a a n.
This means to take the nth root of a.
1
__
Examples: 121 2 121 11
1
__
3 216 3 216 6
1
__
4 256 4 256 4
m
__
m
n
a .
Powers and roots can be expressed using rational exponents a n Examples:
The denominator is the root and
the numerator is the power.
2
__
3 2
2
64 3 64 4 16
4
__
5 4
32 5 32 2 4 16
To write expressions using rational exponents, use the definitions.
1
m
__
__
n n m
n n m
a a n and a a n
a m .
Note that a
3
1
__
__
4 Examples: 5 5 2
6 3 6 4
Think: The root is n 4.
The power is m 3.
Write each expression in radical form and simplify.
3
4
__
__
3 4
7. 27 3 27 8. 49 2
81
2
__
4 3
16 8
3
49 343
Write each expression by using rational exponents.
5 10. 4 2 Think: m 2, n 5 11. 19
45
3
__
9. 16 4
12.
6 5
4
5
__
1
__
19 2
64
Simplify each expression.
24
13. ___
3x 3
3 14. 49 8x 6
1
__
3
2
__
x
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c08-6_rt.indd 47
15.
13
117
____
14x 2
3
47
Holt Algebra 2
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