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Pre-Algebra 5.0 ~ Note Sheets
Chapter 9 Lessons 1 and 2
Square Roots and Real Numbers
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Lesson One: To find square roots and to estimate square roots
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Perfect squares:
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whole numbers
(examples: 25, 49, 81, 100)
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Square root:
a number that is one of two equal
factors of the number
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numbers that are squares of
Radical sign:
,
used to indicate the square
root
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Examples: Find each square root.
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1.
25
2.
 64
3.
4.
0.04
5.
1.96
6.
 36
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13 =
14 =
15 =
 1
Estimate the square root AND give the two integers each square root falls between.
Show your estimation work!
1.
_____ <
8 < _____
2.
_____ <
67 < _____
3.
_____ <
95.3 < _____
estimate: _________ integers: _______________
4.
_____ <  12 < _____
estimate: __________ integers: _______________
5.
_____ <  123 < _____
estimate: _________ integers: _______________
estimate: ___________ integers: _______________
estimate: __________ integers: _______________
Lesson Two: To identify and compare numbers in the real number system
and to solve equations by finding square roots
Natural numbers (Counting numbers):
Whole numbers:
Integers:
1, 2, 3, . . .
0, 1, 2, 3, . . .
. . . , -3, -2, -1, 0, 1, 2, 3, . . .
Rational numbers:
all numbers that can be written in the
a
form b including terminating decimals
and repeating decimals
Irrational numbers:
numbers that cannot be written as a
fraction; numbers that are not
repeating or terminating decimals
(they go on forever with no pattern)
Real Numbers:
the set of rational and irrational numbers
Examples:
Determine whether each statement is sometimes, always, or never true.
1. A rational number is a whole number.
2. Zero is a natural number.
REAL
RATIONAL
INTEGERS
INTEGERS
…, -3, -2, -1, 0, 1, 2, 3,…
IRRATIONAL

WHOLE
0, 1, 2, 3, …
0.1749...
NATURAL
1,2,3,…
2
1
 0 .5
2
1
 0. 3
3
For each number, put an X in the box if it belongs to that set of numbers.
Natural
3.
12
4.
-5
1
9
5.
6.
7.
31
24
8
8.
6.54
9. 0.050050005…
Whole
Integer
Rational
Irrational
Real
Choose the symbol to replace ● to make a true sentence.
10.
9  2 .1
a.
11.
<
b.
=
c.
>
b.
=
c.
>
94.6  10
a.
<
Order the integers in each set from least to greatest.

12. 

1 36

49 , 7 ,
, 7.27 
4 5

Solve each equation. Round to the nearest tenth, if necessary.
Give your answer as an equation.
13. a 2  64
14. e 2  81
15.
f 2  0.49
Work for 9.1 Worksheet:
34.
_____ <
38 < _____
36.
_____ <
389 < _____
estimate: _________ integers: _______________
38.
_____ < 118 < _____
estimate: _________ integers: _______________
40.
_____ <  83 < _____
42.
_____ <  119 < _____
44.
_____ <
estimate: _________ integers: _______________
estimate: _________ integers: _______________
estimate: _________ integers: _______________
27.5 < _____ estimate: _________ integers: _______________
Work for 9.2 Worksheet:
Natural
2.
4.
25
1
8
6.
0.343434…
8.
10.
7
32

4
12.
24.6
14.
0
Whole
Integer
Rational
Irrational
Real