QUOTIENT PROPERTY OF RADICALS
a
where a ≥ 0 and b > 0
ba b
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INT
2
EXAMPLE
Student Help
Example:
9
3
295 5
2
5
Simplify with the Quotient Property
5320
Simplify .
Solution
2 p 16
5320 2p2
5
Factor using perfect square factors.
1265
Divide out common factors.
16
25
Use quotient property.
4
5
Simplify.
In Example 3 you will see how to eliminate a radical from the denominator by
multiplying the radical expression by an appropriate value of 1. This process is
called rationalizing the denominator.
3
EXAMPLE
Student Help
Rationalize the Denominator
118
STUDY TIP
1
2
and are
2
2
Simplify .
equivalent radical
expressions. The
second expression is
in simplest form with a
rational denominator.
Solution
1
118 18
Use quotient property.
1
9 p 2
Use product property.
1
32
Remove perfect square factor.
1
32
p
2
2
6
2
2
Multiply by a value of 1: 1.
Simplify: 32
p 2
3 p 2 6.
Simplify with the Quotient Property
Simplify the expression.
5.
512
Chapter 9
49
Quadratic Equations and Functions
1
6. 5 25
7.
13
8.
1275