Chp 8 Workbook
Chp 8 Workbook
Chp 8 Workbook
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NAME DATE PERIOD<br />
8-1<br />
Study Guide and Intervention<br />
Geometric Mean<br />
Geometric Mean The geometric mean between two numbers is the positive square<br />
root of their product. For two positive numbers a and b, the geometric mean of a and b is<br />
the positive number x in the proportion −<br />
a x = −<br />
x b . Cross multiplying gives x2 = ab, so x = √ ab .<br />
Example<br />
Find the geometric mean between each pair of numbers.<br />
a. 12 and 3<br />
x = √ ab<br />
= √ 12 . 3 a = 12 and b = 3<br />
Definition of geometric mean<br />
= √ (2 . 2 . 3) . 3 Factor.<br />
= 6 Simplify.<br />
The geometric mean between 12 and 3 is 6.<br />
b. 8 and 4<br />
x = √ ab<br />
= √ 8 . 4 a = 8 and b = 4<br />
= √ (2 . 4) . 4 Factor.<br />
= √ 16 . 2 Associative Property<br />
Definition of geometric mean<br />
= 4 √ 2 Simplify.<br />
The geometric mean between 8 and 4<br />
is 4 √ 2 or about 5.7.<br />
Lesson 8-1<br />
Exercises<br />
Find the geometric mean between each pair of numbers.<br />
1. 4 and 4 2. 4 and 6<br />
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.<br />
3. 6 and 9 4. 1 −<br />
2 and 2<br />
5. 12 and 20 6. 4 and 25<br />
7. 16 and 30 8. 10 and 100<br />
9. −<br />
1 2 and −<br />
1 4<br />
10. 17 and 3<br />
11. 4 and 16 12. 3 and 24<br />
Chapter 8 5 Glencoe Geometry
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