Simplifying Radical Expressions Worksheet
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1
2NAME
DATE
PERIOD
10-2
Study Guide and Intervention
Simplifying Radical Expressions
Product Property of Square Roots
The Product Property of Square Roots and
prime factorization can be used to simplify expressions involving irrational square roots.
When you simplify radical expressions with variables, use absolute value to ensure
nonnegative results.
√
√
Product Property of Square Roots
For any numbers a and b, where a ≥ 0 and b ≥ 0,
ab = √ a
b .
Example 1
Simplify √ 180 .
√ 180 = √ 2 2 3 3 5
Prime factorization of 180
= √ 2
√ 3
√ 5
2
2
Product Property of Square Roots
= 2 3 √ 5
Simplify.
= 6 √ 5
Simplify.
√
Example 2
Simplify
120a
2
· b
5
· c
4
.
√ 120a
2
b
5
c
4
= √ 2
3
3 5 a
2
b
5
c
4
= √ 2
√ 2
√ a
√ b
√ c
2
√ 3
√ 5
2
4
4
b
= 2 √ 2
√ 3
√ 5
√ b c
a
b
2
2
⎪
⎥
√ 30b
2
2
= 2
a
b
c
⎪
⎥
Exercises
Simplify each expression.
1. √ 28
2. √ 68
3. √ 60
4. √ 75
5. √ 162
6. √ 3
√ 6
7. √ 2
√ 5
8. √ 5
√ 10
·
·
·
9. √ 4a
10. √ 9x
11. √ 300a
12. √ 128c
2
4
4
6
14. √ 3x
3 √ 3x
15. √ 20a
13. 4 √ 10 3 √ 6
√
2
4
2
b
4
16.
100x
3
y
17. √ 24a
19. √ 150a
√
4
b
2
18.
81x
4
y
2
2
b
2
c
20. √ 72a
√
√
6
b
3
c
2
21.
45x
2
y
5
z
8
22.
98x
4
y
6
z
2
11
Glencoe Algebra 1
Chapter 10
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