Evaluate expressions containing square roots.

1
Objectives
Evaluate expressions containing square
roots. Classify numbers within the real number
system.
2
Vocabulary
square root terminating decimal perfect square
repeating decimal real numbers irrational
numbers natural numbers whole numbers integers rat
ional numbers
3
A number that is _____________to form a product
is called a square root of that product. The
operations of squaring and finding a square root
are _____________
The radical symbol , is used to represent
square roots. Positive real numbers have
two square roots.
Positive square root of 16
4
4 ? 4 42 16
4

(4)(4) (4)2 16
Negative square root of 16
4
The nonnegative square root is represented by
. The negative square root is represented by
.
A perfect square is a number whose positive
square root is a whole number. Some examples of
perfect squares are shown in the table.
0
1
100
4
9
16
25
36
49
64
81
02
12
22
32
42
52
62
72
82
92
102
5
(No Transcript)
6
Example 1 Finding Square Roots of
Perfect Squares

Find each square root.
Think What number squared equals 16?
42 16
Positive square root positive 4.
Think What is the opposite of the square root
of 9?
32 9
Negative square root negative 3.
7
Example 1C Finding Square Roots of
Perfect Squares

Find the square root.
8
Check It Out! Example 1
Find the square root.
Think What number squared equals 4?
Think What is the opposite of the square root of
25?
.
9
The square roots of many numbers like , are
not whole numbers. A calculator can approximate
the value of as 3.872983346... Without a
calculator, you can use square roots of perfect
squares to help estimate the square roots of
other numbers.
10
Example 2 Problem-Solving Application
As part of her art project, Shonda will need to
make a square covered in glitter. Her tube of
glitter covers 13 square inches. What is the
greatest side length Shondas square can have?
The answer will be the side length of the square.
List the important information
The tube of glitter can cover an area of 13
square inches.
11
Example 2 Continued
12
Example 2 Continued
13
Example 2 Continued
Guess 3.6 3.62 12.96 too low
Guess 3.7 3.72 13.69 too high
3.6
3.7
4
3
14
Example 2 Continued
A square with a side length of 3.6 inches would
have an area of 12.96 square inches. Because
12.96 is close to 13, 3.6 inches is a reasonable
estimate.
15
All numbers that can be represented on a number
line are called real numbers and can be
classified according to their characteristics.
16
Natural numbers are the counting numbers 1, 2,
3,
Whole numbers are the natural numbers and zero
0, 1, 2, 3,
Integers are whole numbers and their opposites
3, 2, 1, 0, 1, 2, 3,
17
Terminating decimals are rational numbers in
decimal form that have a finite number of
digits 1.5, 2.75, 4.0
18
Example 3 Classifying Real Numbers
Write all classifications that apply to each
Real number.
A. 32
B. 5
19
Check It Out! Example 3
Write all classifications that apply to each real
number.
3b. 12
20
Lesson Quiz
Find each square root.

3.
4.

1.
2.
5. The area of a square piece of cloth is 68 in2.
How long is each side of the piece of cloth?
Round your answer to the nearest tenth of
an inch.
Write all classifications that apply to each real
number.
6. 1
8.