Download Algebra 1 Lesson Notes 2.7

Algebra 1
Lesson Notes 2.7A
Date _______________
Objective: Find square roots.
Square Root of a number: If b2 = a, then b is a square root of a.
Notation:
a indicates the square root of a.
radical symbol
a
radicand
All positive real numbers have two square roots, one positive square root (the principal square
root) and one negative square root.
The square of 7 is 72 = 49. The square of –7 is (–7)2 = 49.
Note: This is a very important detail.
To square a negative number, you MUST use parentheses!
 a indicates the positive and negative square roots
a indicates the positive square root
 a indicates the negative square root
Zero has one square root, 0.
Negative real numbers have no real square roots. Why?
Example 1 (p 110): Find square roots
a.
 36
b.
144
c.
400
d.
 28
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Perfect Squares: The square of a number is called its perfect square.
Conversely, a number is a perfect square if its square roots are integers.
Helpful advice: Become familiar with perfect squares!!! List the squares of 1-20.
Example 2 (p 111): Approximate a square root
The cover of a square box has an area of 220 sq. in. Estimate the length
of a side of the cover to the nearest inch.
Notation: ≈ indicates approximately equal to
 HW
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A7 pp 113-116 #4-14 even, 15-23, 47-48
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Algebra 1
Lesson Notes 2.7B
Date _______________
Objective: Compare real numbers.
irrational number: a number that cannot be written as a quotient of two
integers.
The decimal form of an irrational number does not terminate and does not repeat.
Real numbers
Rational numbers
2
5
0
−1.65
Irrational numbers
Integers
49
−3
7
3
21
20
Whole numbers
14
0
−9
Example 5: Rewrite a conditional statement in if-then form
Tell whether the statement is true or false. If false, give a counterexample.
a.
b.
c.
d.
No integers are irrational numbers.
All real numbers are rational numbers.
No square roots are rational numbers.
All integers are rational numbers.
 CW: p 114 #30-33 (Using the Venn diagram to make conclusions)
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Example 3 (p 112): Classify numbers
Classify each of the following numbers.
Real
number
Number
Rational
number
Irrational
number
Integer
number
Whole
number
 25
100
30
Example 4 (p 112) Graph and order real numbers
Order the numbers from least to greatest:  10 ,
−5
 HW
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−4
−3
−2
−1
0
19
, – 3,
5
1
2
16 ,
12
3
A8 pp 113-116 #24-28 even, 34-42, 49-50, PQ 2.6-2.7 #1-6
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