Download 1-8B Square Roots and 1

1-8 Number Systems
Square Roots
Add
closure
property?
You will be allowed to use a calculator for tomorrow’s lesson but
NOT on the CHAPTER 1 test! NO GRAPHING CALCULATORS!
Algebra 1
Glencoe McGraw-Hill
Linda Stamper
REAL NUMBERS
Rational Numbers: Any number that can be
a
written in the form of . As a decimal they repeat or
b
terminate.
1
ex:
= 0.3333... Repeats
3
ex: 1 = 0.25 Terminates
4
Integers: Whole numbers and their opposites
(this means positive and negative whole numbers).
ex: … ‫ ־‬4 ,‫ ־‬3 ,‫ ־‬2 ,‫ ־‬1 ,0 ,1 ,2 ,3 ,4 …
Whole Numbers: Natural Numbers and
zero. ex: 0,1,2,3…
Natural or Counting Numbers
ex: 1,2,3,4,…
Irrational
Numbers:
ex:
 and 2
These must
be
represented
by a symbol
(ex: ), or as a
rounded
number, or in
radical form
because the
decimal
doesn’t repeat
or terminate
(stop).
You will need a calculator for today’s lesson.
While you are allowed to use a calculator for
today’s lesson, you will NOT be allowed to use
one on the CHAPTER 1 test!
NO GRAPHING CALCULATORS!
You must learn how to use a calculator! There are many
makes and models. Read the instruction booklet.
Enter a problem into the calculator for which you
already know the answer. For example: 4
2nd √ 4
=
2
Keystrokes for
TI-30X IIS
4
√
=
2
Keystrokes for
TI-30X A
Example 1 Evaluate the expression. Give the exact value,
if possible. Otherwise, approximate to the nearest
hundredth. You may use a calculator for this section.
2nd √ 8
=
8  2.83
What is the positive square root of 8?
Keystrokes for
TI-30X IIS
Example 1 Evaluate the expression. Give the exact value,
if possible. Otherwise, approximate to the nearest
hundredth. You may use a calculator for this section.
8
√
=
8  2.83
What is the positive square root of 8?
Keystrokes for
TI-30X A
Evaluate the expression. Give the exact value, if possible.
Otherwise, approximate to the nearest hundredth. You
may use a calculator for this section.
Example 2
 11  3.32
What is the negative square root of 11?
Example 3
 1.69  1.3
What is the positive and negative square
root of 1.69?
To compare real numbers, find a decimal approximation for
each number and then compare.
19  3.8
4.3588989...  3.88888...
The inequality
symbol points
to the smaller
value!
The three dots are
an ellipsis. In math,
an ellipsis is used to
indicate that the
numbers continue in
the same pattern.
Replace each
with <, >, or = to make a true statement.
Example 4
2
2

3
5
2.666...  2.23506...
Example 6
72  7.8
8.4852... 
7.8888...
Example 5
8
0.8  9
0.8888...  0.88888...
Example 7
48  6.9
6.92820... 
6.9999...
Order from least to greatest.
Example 9
Example 8
1
8
53

1
.
46
,
0
.
2
,
2
,
and

2.63,  7, , and
6
3
 20
 1.46  1.464646...
2.63  2.636363...
 7  2.64575...
0.2  0.20000...
8
 2.6666...
2  1.4142135...
3
1
53
  0.166666...
 2.65
6
 20
1
53
8

1
.
46
,

, 0.2, 2
,  7, 2.63,
6
 20
3
Remember: To compare real numbers, find a decimal
approximation for each number and then compare.
1-9 Coordinate Plane
All coordinate plane graphs must
be completed on grid paper.
A coordinate plane is formed by two real number lines that
intersect at a right angle at the origin. The horizontal axis
is the x-axis and the vertical axis is the y-axis.
y
The coordinate plane is
divided into four regions
called quadrants.
II
•
I
III IV
x
Each point in a coordinate plane corresponds to an
ordered pair of real numbers. (–2,3)
The first number
identifies the
x-coordinate and
the second
number identifies
the ycoordinate.
•
x
y
Graph the coordinate (3,4).
The first number
identifies the
x-coordinate and
the second
number identifies
the y-coordinate.
•
x
y
Example 1 Graph the coordinate (4,–2).
The first number
identifies the
x-coordinate and
the second
number identifies
the ycoordinate.
x
•
y
Example 2 Graph and label the coordinates in the same
coordinate plane:
A (3,–1), B (–4,0), C (–5,2),
D (2,–4), E (0,3), F (0,0).
C
•
E
•
B
•
•
F
•A
•D
y
x
Example 3 In which quadrant or on which axis does
each ordered pair lie?
A.
B.
C.
D.
E.
F.
G.
H.
IV
x-axis
II
IV
y-axis
origin
III
I
C
•
E
•
•
B
F
•
•
G
H
•
•A
•D
y
x
Example 4 Write the coordinates of each point.
•
D
•
G
•
B
C
•
•
F
E
•
y
•A
A
B
C
x D
E
F
G
(3,–2)
(–4,0)Coordinates
(–5,–2)
are written as
(2,4)
ordered pairs.
(0,–3)
You must use
(0,0)parentheses!
(–4,3)
1-A13 Pages 50-52 # 22–27,38-41,56-59,73-75.
(Scientific calculators OK).