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Math 009 Unit 4 Lesson 4 - PowerPoint PPT Presentation


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Math 009 Unit 4 Lesson 4. By definition Ö 25 is the number you would multiply times itself to get 25 for an answer. . Because we are familiar with multiplication, we know that Ö 25 = 5. Numbers like 25, which have whole numbers for their square roots, are called perfect squares.

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slide2

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

slide3

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

slide4

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

slide5

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

slide6

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

slide7

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

slide8

Simplify the following expressions

-Ö4

=

-2

=

7 8 + 9

·

7Ö64 + 9

=

56 + 9

= 65

5 +

=

5 5 + 7

·

Ö25

Ö49

=

25 + 7

= 32

slide9

Simplify the following expressions

Ö

4

Ö4

2

=

=

81

Ö81

9

1

1

Ö

1

Ö

1

=

12

6

36

144

1

2

=

12

12

1

=

12

slide10

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

·

slide11

Graphing real numbers

The graph of a number is a dot placed where the number would be on the number line

12

Graph the number: 3

-10

-5

0

5

10

Graph the number: -8.5

-10

-5

0

5

10

slide12

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

(

)

-10

-5

0

5

10

Graph the real numbers less than 8

)

-10

-5

0

5

10

slide13

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 > -3

(

-10

-5

0

5

10

Graph the inequality: x £4

]

-10

-5

0

5

10