Download square root

1.3 – Real Numbers and the
Number Line
I.SQUARES and SQUARE
ROOTS:
The term square root comes from the AREAS
of squares and their sides.
3
3
Because 9 = 32, we say that 3 is a SQUARE
ROOT of 9
In general, if A = s2, then s is called a square root of A
The symbol for the
is called the RADICAL.
The expression under the radical is the RADICAND.
Together they form the SQUARE ROOT.
Squares and Square Roots you should know:
x 1 2 3 4
x2 1 4 9 16
5
25
6 7 8 9 10 11 12 13 14 15
36 49 64 81 100 121 144 169 196 225
Examples: Simplify the following:
1) 36
6
2)
169
13
3)
64
9
4)
8
3
1
625
1
25
The square of an integer is a PERFECT SQUARE.
To estimate a perfect square, find the two nearest perfect
squares and determine which is closer.
Estimate the square root. Round to the nearest integer.
1) 10
3
2)
6
38
3)
9
84
4)
7
50
II. Sets of numbers
A SET is a well defined collection of objects.
Each object is called an ELEMENT of the set.
A SUBSET of a set consists of elements from
the given set.
You can list the elements of a set between
BRACES: { }
Frequently Used Sets of Numbers
Natural Numbers: 1, 2, 3, 4,…
Whole Numbers: 0, 1, 2, 3, 4,…
Integers: …, -2, -1, 0, 1, 2, …
1
3
5
Rational Numbers: … 2,  , 0, , ,...
2 4 3
Irrational Numbers: … 2,  ,1.4114111411114...
Rational Numbers include any terminating or
repeating decimal numerals.
Rational numbers include any number that
a
can be written in the form b , where a and b
are both integers where b  0.
Irrational Numbers include infinite nonrepeating decimals.
Real numbers include all rational and
irrational numbers.
Natural
Whole
Integers
Rational
Irrational
Real
The square of an integer is a PERFECT SQUARE.
To estimate a perfect square, find the two nearest perfect
squares and determine which is closer.
Name the subset(s) of the real numbers to which each number
belongs.
1) 77
Irrational
Real
2) 4
Natural
Whole
Integer
Rational
Real
3)
2
3
Rational
Real
4)
0
Whole
Integer
Rational
Real
Comparing Real Numbers:
An INEQUALITY is a mathematical sentence the compares
the values of two expressions using an inequality symbol.
Less than

Greater than

Less than or
equal to

Greater than
or equal to

Example:
Compare the following with an inequality symbol
1
17 and 4
3
1) Rewrite as decimal:
17  4.123...
1
4  4.333...
3
2) Compare the decimals:
4.123...
4.333...
3) Write using an inequality:
1
17 <4
3
Example:
Compare the following using a number line:
1
3
1.5, 2.6, 4, 2 , and 
3
4
1) Rewrite as decimals:
1.5, 2.6, 2, 2.33333,  0.75
2) Plot on a number line:
2
1
0
1.5  0.75
3) Write using an inequality:
1.5  
1
2
3
2 2.33333 2.6
3
1
 4  2 <2.6
4
3
Homework :
TUESDAY:
Section 1.3
pages 23-25
#’s 1-8, 10, 14, 16, 17, 20, 22, 23, 26, 29,
33, 37, 41
WEDNESDAY:
#’s 13, 19, 25, 29, 34, 40, 42, 46, 48, 60, 65,
66, 67, 68