Download Alg 1 2-7 Power Point

Algebra 1 Notes:
Lesson 2-7:
Square Roots and Real
Numbers
Objectives
• Distinguish between Rational and
Irrational Numbers
• Graph sets of Real Numbers on the
number line
• Organize Real Numbers into numerical
order
Vocabulary
• Square Root
One of two equal factors of a number
• Perfect Square
• Radical Sign
Vocabulary
• Square Root
One of two equal factors of a number
• Perfect Square
Solution of any number squared
• Radical Sign
Vocabulary
• Square Root
• Perfect Square
• Radical Sign
If it comes in the problem, it only wants
the positive solution.
64  8
Indicates the principal
square root of 64
 64  8
Indicates the negative
square root of 64
 64  8
Indicates both square
roots of 64
Example 1
Find each square root.
a)  16 =
9
b)
1
±1
3
0.0144
Example 1
Find each square root.
a)  16 =
9
b)
1
±1
3
0.0144 = 0.12
Vocabulary
•Irrational Numbers
examples….
• Real Numbers
Vocabulary
•Irrational Numbers
examples….
• Real Numbers
- Any number on the number line.
- Every number you know about.
Real Numbers
Rational Numbers
Integers
Whole
Numbers
Natural
Numbers
Irrational
Numbers
Example 2
Name the set or sets of numbers to
which each real number belongs.
a) 17
Example 2
Name the set or sets of numbers to
which each real number belongs.
a) 17 = 4.1231056…
Example 2
Name the set or sets of numbers to
which each real number belongs.
a) 17 = 4.1231056…
b)
1
6
Irrational
number
Example 2
Name the set or sets of numbers to
which each real number belongs.
a) 17 = 4.1231056…
b)
1
6
c) 169
Irrational
number
Rational number
Example 2
Name the set or sets of numbers to
which each real number belongs.
a) 17 = 4.1231056…
b)
1
6
c) 169 = 13
Irrational
number
Rational number
Example 2
Name the set or sets of numbers to
which each real number belongs.
a) 17 = 4.1231056…
b)
1
6
c) 169 = 13
d) -327
Irrational
number
Rational number
Rational, integer,
whole, natural
Example 2
Name the set or sets of numbers to
which each real number belongs.
a) 17 = 4.1231056…
b)
1
6
c) 169 = 13
Irrational
number
Rational number
Rational, integer,
whole, natural
d) -327 Rational number and integer
Example 3
Graph each solution set.
a) x > -2
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
0
1
2
3
4
5
6
7
8
9
10
Example 3
Graph each solution set.
a) x > -2
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
0
1
2
3
4
5
6
7
8
9
10
Example 3
Graph each solution set.
a) x > -2
b) a ≤ 4.5
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
0
1
2
3
4
5
6
7
8
9
10
Example 3
Graph each solution set.
a) x > -2
b) a ≤ 4.5
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
0
1
2
3
4
5
6
7
8
9
10
Example 4
Replace each _____ with <, >, or = to
make each sentence true.
a) 14
196
Example 4
Replace each _____ with <, >, or = to
make each sentence true.
a) 14
196 = 14
Example 4
Replace each _____ with <, >, or = to
make each sentence true.
a) 14
b) 48
=
196 = 14
6.9
Example 4
Replace each _____ with <, >, or = to
make each sentence true.
a) 14
b) 48
=
196 = 14
6.9
48 = 6.9282032…
Example 4
Replace each _____ with <, >, or = to
make each sentence true.
a) 14
b) 48
=
196 = 14
6.9
48 = 6.9282032…
6.9 = 6.9999999…
Example 4
Replace each _____ with <, >, or = to
make each sentence true.
a) 14
=
b) 48
<
196 = 14
6.9
48 = 6.9282032…
6.9 = 6.9999999…
Example 5
8
2.
63
,
7
,
Write
3,
least to greatest.
53
-20
in order from
2.63 = 2.63636363…
 7 = -2.64575131…
8
3
= 2.66666666…
53
 20
53
 20
= -2.65
,  7 , 2.63 ,
8
3
Homework
Pgs. 107: 20 – 56 (evens)