Math 009 Unit 4 Lesson 4

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Math 009 Unit 4 Lesson 4
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By definition Ö25 is the number you would
multiply times itself to get 25 for an answer.
Because we are familiar with multiplication, we
know that Ö25 5
Numbers like 25, which have whole numbers for
their square roots, are called perfect squares
You need to memorize at least the first 15
perfect squares
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Square root
Square root
Perfect square
Perfect square
1
81
Ö1 1
Ö81 9
4
100
Ö4 2
Ö100 10
9
121
Ö9 3
Ö121 11
16
144
Ö16 4
Ö144 12
25
169
Ö25 5
Ö169 13
36
196
Ö36 6
Ö196 14
49
225
Ö49 7
Ö225 15
64
Ö64 8
4
Every whole number has a square root
Most numbers are not perfect squares, and so
their square roots are not whole numbers.
Most numbers that are not perfect squares have
square roots that are irrational numbers
Irrational numbers can be represented by decimals
that do not terminate and do not repeat
The decimal approximations of whole numbers can
be determined using a calculator
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Obj To find the square root of a number

• Find the square roots of the given numbers

• If the number is not a perfect square, use a
  calculator to find the answer correct to the
  nearest thousandth.

81
Ö81 9
37
Ö37 6.083
158
Ö158 12.570
6
Obj To find the square root of a number

• Find two consecutive whole numbers that the
  given square root is between

• Try to do this without using the table

Ö16 4 and Ö25 5 so
Ö18
Ö18 is between 4 and 5
Ö115
Ö100 10 and Ö121 11 so
Ö115 is between 10 and 11
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Multiplying radicals
The product of the square roots of two numbers is
the same as the square root of the product of the
numbers
Examples
Ö3


Ö12
Ö36
Ö7


Ö11
Ö77
8

Simplify the following expressions
-Ö4

-2


7 8 9
7Ö64 9

56 9
65
5


5 5 7
Ö49
Ö25

25 7
32
9

Simplify the following expressions
Ö
4
2
Ö4


81
9
Ö81
1
1
Ö
1
Ö
1



12
6
36
144
1
2


12
12
1

12
10
Simplified radical form
No factor inside the radical should be a perfect
square.
Ö18


Ö2
3
Ö2

Ö9 2
Ö9

Ö108


Ö3
6
Ö3

Ö36 3
Ö36

Ö96


Ö6
4
Ö6

Ö16 6
Ö16

11
Graphing real numbers
The graph of a number is a dot placed where the
number would be on the number line
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Graph the number 3
0
5
10
-5
-10
Graph the number -8.5
0
5
10
-5
-10
12
Graphing inequalities
The symbol, , means that the point is
included in the graph
The symbol, ( , means that the point is not
included in the graph
Graph the real numbers between -4 and 6
(
)
0
5
10
-5
-10
Graph the real numbers less than 8
)
0
5
10
-5
-10
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Graphing inequalities
The symbol, , means that the point is
included in the graph
The symbol, ( , means that the point is not
included in the graph
Graph the inequality x gt -3
(
0
5
10
-5
-10
Graph the inequality x 4

0
5
10
-5
-10