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# Algebra C & A Extra Examples Lesson 13-1 by qfAcYv

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```									Geometry Concepts and Applications                                                              Chapter 13

Lesson 13-1

Examples                Simplify each expression.
1    169                                      2     625
169 = 13 because 132 = 169.                    625 = 25 because 252= 625.

Example             3   Simplify 72.
72 = 2  2  2  3  3        The prime factorization of 72 is 2  2  2  3  3.
Use the Product Property of Square Roots
= 2      22     33
to group any factors that occur in pairs.
= 223                     2  2 = 4 or 2 and 3  3 = 9 or 3
= 2  6 or 6 2             6 2 means 6 times 2.

Example             4   Simplify 7  14.
7  14 = 7  14               Product Property of Square Roots
= 772                Replace 14 with 7  2.
= 77 2               Product Property of Square Roots
= 7  2 or 7 2          7  7= 7

Examples                Simplify each expression.
42                                               25
5                                             6
7                                                49
42     42                                        25     25
=             Quotient Property                   =         Quotient Property
7      7                                         49     49
= 6                                              5
=
7

Example                              11
7   Simplify       .
7
11    11     7        7
=                   =1
7      7     7        7
11  7
=                Product Property of Square Roots
77
77
= 7                77=7
Geometry Concepts and Applications                                                          Chapter 13

Example                            5
8   Simplify     .
10
5     5    10          10
=                     =1
10    10   10          10
5  10
=                 Product Property of Square Roots
10  10
5 10
=
100
5 10
= 10                100 = 10
10             5   1
= 2                 =
10 2

Example             9   The area of a square can be found by using the formula A = s2, where s is the
length of a side. Suppose the area of a square is 98 square centimeters. Find
the length of a side in simplest radical form and as a decimal rounded to the
nearest tenth.
A = s2      Formula for the area of a square
2
98 = s       Replace A with 98.
98 = s       Take the square root of each side.
772 =s          Product Property of Square Roots
7 2 =s

To find the decimal approximation for the side length, use a calculator.
7  [ ] 2  9.899494937

The simplest radical form for the length of a side is 7 2 centimeters and the
decimal approximation is 9.9 centimeters.

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