Simplifying Radical Expressions Worksheet Page 2
ADVERTISEMENT
1
2NAME
DATE
PERIOD
10-2
Study Guide and Intervention
(continued)
Simplifying Radical Expressions
Quotient Property of Square Roots
A fraction containing radicals is in simplest
form if no radicals are left in the denominator. The Quotient Property of Square Roots
and rationalizing the denominator can be used to simplify radical expressions that
involve division. When you rationalize the denominator, you multiply the numerator and
denominator by a radical expression that gives a rational number in the denominator.
a
a
√
√
Quotient Property of Square Roots
For any numbers a and b, where a ≥ 0 and b > 0,
−
=
−
.
b
√ b
Example
√
56
Simplify
−
.
45
56
4 14
√
√
−
=
−
Factor 56 and 45.
45
9 5
2 √ 14
=
−
Simplify the numerator and denominator.
3 √ 5
2 √ 14
√ 5
⎯⎯
5
√
=
−
−
−
Multiply by
to rationalize the denominator.
⎯⎯
5
3 √ 5
√ 5
√
2 √ 70
=
−
Product Property of Square Roots
15
Exercises
Simplify each expression.
√ 9
√ 8
1.
−
2.
−
√ 18
√ 24
√ 100
√ 75
3.
−
4.
−
√ 121
√ 3
8 √ 2
6
√
2
√
5.
−
6.
−
−
5
5
2 √ 8
√
3
√
5
√
5
2
√
7.
−
−
8.
−
−
4
2
7
5
2
6
√
3a
√
x
9.
−
10.
−
10b
6
y
4
100a
4
75b
3
c
6
√
√
11.
−
12.
−
8
2
144b
a
√ 4
√ 8
13.
−
14.
−
3 - √ 5
2 + √ 3
√ 5
√ 8
15.
−
16.
−
5 + √ 5
2 √ 7 + 4 √ 10
12
Glencoe Algebra 1
Chapter 10
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education