DATE
NAME
13-2
Student Edition
Pages 719–725
Study Guide
Simplifying Radical Expressions
The product property of square roots and prime factorization
can be used to simplify irrational square roots. When you
simplify radical expressions with variables, use absolute values
to ensure nonnegative results.
Example 1: Simplify Ï180 .
Ï180 5
5
5
5
Example 2: Simplify Ï100a2 .
Ï2 ? 2 ? 3 ? 3 ? 5
Ï2 ? 2 ? Ï3 ? 3 ? Ï 5
2 ? 3 ? Ï5
6Ï5
Ï100a2 5 Ï100 ? Ïa2
5 10)a)
Use the quotient property of square roots and a method called
rationalizing the denominator when simplifying radical
expressions involving division. Study the example below.
!
56
Example 3: Simplify 45.
!45 5 Ï45
Ï56
56
5
2 ? Ï14
3 ? Ï5
5
2Ï14
3Ï5
?
Ï5
Ï5
5
2Ï70
15
Simplify. Leave in radical form and use absolute value
symbols when necessary.
1. Ï18
2. Ï68
3. Ï60
4. Ï75
5. Ï162
6. Ï4a2
7. Ï9x4
8. Ï300a4
9. Ï128c6
13.
–
Ï9
—
Ï18
17.
—
Ï75
–
Ï3
© Glencoe/McGraw-Hill
10. Ï5 ? Ï10
14.
–
Ï8
—
Ï24
18.
–
8Ï2
–
2Ï8
11. Ï3x2 ? 3Ï3x4
15.
19.
89
–
Ïx6
–
Ïy4
–
Ï4
–
3
2
Ï5
12. 4Ï10 ? 3Ï6
16.
20.
–
Ï100
–
Ï8
–
—
2Ï7 1 4Ï10
Algebra 1