To view this presentation, you'll need to enable Flash.

Show me how

After you enable Flash, refresh this webpage and the presentation should play.

Loading...

PPT – Squares PowerPoint presentation | free to download - id: 5b8d58-ZTYxN

The Adobe Flash plugin is needed to view this content

View by Category

Presentations

Products
Sold on our sister site CrystalGraphics.com

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Squares Square Roots

Area 9 u2

- Algebra-A

side 3 u

Why are some numbers called square numbers?

1

4

9

. . .

16

and others are not called squares?

. . .

2

3

10

The answer involves the SHAPES you see below!

1

4

9

. . .

16

Along with the FACTORS involved!

. . .

2

3

10

Is a square possible. . .

If YES, then the number is a SQUARE number!

given 1 square unit?

YES! 1 x 1 1

12

given 4 square units?

YES! 2 x 2 4

22

given 9 square units?

YES! 3 x 3 9

32

given 16 square units?

YES! 4 x 4 16

42

. . .

Is a square possible. . .

Can you see how FACTORS are involved?

given 2 square units?

NO!

2 1 x 2 OR 2 x 1

given 3 square units?

NO!

3 1 x 3 OR 3 x 1

given 5 square units?

NO!

5 1 x 5 OR 5 x 1

given 6 square units?

NO!

6 1 x 6 OR 6 x 1

Only RECTANGLES are possible here!

. . .

6 2 x 3 OR 3 x 2

Why are some numbers called square numbers?

A number is a perfect square if you can build

a rectangle that is a square using the exact

given number of square units!

Why are some numbers called square numbers?

So, there are perfect squares, and then there

are squares that can be formed, but not

perfectly made!

Perfect rectangles, but NOT perfect

squares!

Is a square possible given 2 square units?

2 1 x 2 OR 2 x 1

So lets take 2 square units and try to build a

square.

Then arrange those parts around this square.

Well have to divide this one into smaller parts.

Perfect rectangles, but NOT perfect

squares!

Is a square possible given 2 square units?

2 1 x 2 OR 2 x 1

So now, each side of our square in progress is

1.4 units.

1.4

0.2

But, we still do not have a complete square!

1

Well have to keep dividing up the remaining part

and add it to our figure until we have a finished

square.

Are you sensing some imperfection yet?

Perfect rectangles, but NOT perfect

squares!

Is a square possible given 2 square units?

2 1 x 2 OR 2 x 1

0.2

1

1.4

I dont know about you, but I think that dividing

up that last bar seems like it will be a VERY

tedious task!

Sure, we could fill in that big gap with some of

it, but them well have to literally shave the

remaining part and apply it equally so that the

two sides we are adding to get equal amounts.

But well fill in the gaps we have so far.

Perfect rectangles, but NOT perfect

squares!

Is a square possible given 2 square units?

2 1 x 2 OR 2 x 1

0.2

1

1.4

I think weve done enough to show that a PERFECT

square is impossible, given 2 square units!

By the way, what is the area of a square with

sides of 1.4 units?

(1.4 units)2 1.96 units2 2 units2

Thats close enough for me!

Perfect squares?

Can you see how FACTORS are involved?

Is a square possible given 2 square units?

2 1 x 2 OR 2 x 1

1.4

A 1.96 2

Only perfect RECTANGLES , but NOT PERFECT

SQUARES!

So from now on, when you are asked if you can

build a square, we are asking whether you can

build a PERFECT SQUARE!

Lets check the number 12!

Given 12 square units, lets see if we can build

a square.

So, this is a 12 x 1 rectangle, which can be

rotated to become a 1 x 12.

1

1

12

12

Lets check the number 12!

Factors 1, 2, 3, 4, 6, 12

Given 12 square units, lets see if we can build

a square.

Now we have a 1 x 12, a 12 x 1, a 2 x 6, a 6

x 2, a 3 x 4, and a 4 x 3.

2

4

6

2

3

3

6

4

Factors of 12

1, 2, 3, 4, 6, 12

1 x 12

2 x 6

3 x 4

Factors of 12

Going up

Going down

Did you notice that as the first factor

increases, the second factor decreases?

1 2 3

12 6 4

consecutive

And there is no whole factor between 3 4.

Factors of 16

1, 2, 4, 8, 16

We only list the 4 once!

Going up

Going down

1 2 4

16 8 4

This time a factor pair is the SAME number!

SAME!

4 x 4 42

16 is a perfect square!

Which numbers are perfect squares?

1, 4, 9, 16, 25, 36, 49, 64, 81, 100,

121, 144, 169

In the first 169 natural numbers, only 13 are

PERFECT SQUARES.

1, 4, 9, 16, 25, 36, 49, 64, 81, 100,

121, 144, 169

1, 2, 3, 4, 5, 6,

7, 8, 9, 10, 11, 12, 13,

14, 15, 16, 17, 18, 19, 20,

21, 22, 23, 24, 25, 26, 27, 28,

29, 30, 31, 32, 33, 34, 35,

36, 37, 38, 39, 40, 41, 42, 43,

44, 45, 46, 47, 48, 49, 50,

51, 52, 53, 54, 55, 56, 57, 58,

59, 60, 61, 62, 63, 64, 65,

66, 67, 68, 69, 70, 71, 72, 73,

74, 75, 76, 77, 78, 79, 80,

81, 82, 83, 84, 85, 86, 87, 88,

89, 90, 91, 92, 93, 94, 95,

96, 97, 98, 99, 100, 101, 102, 103, 104,

105, 106, 107, 108, 109, 110, 111, 112, 113,

114, 115, 116, 117, 118, 119, 120 121, 122, 123,

124, 125, 126, 127, 128, 129, 130, 131, 132,

133, 134, 135, 136, 137, 138, 139, 140, 141,

142, 143, 144, 145, 146, 147, 148, 149, 150, 151,

152, 153, 154, 155, 156, 157, 158, 158, 159,

160, 161, 162, 163, 164, 165, 166, 167, 168,

169 . . .

1, 2, 3, 4, 5, 6,

7, 8, 9, 10, 11, 12, 13,

14, 15, 16, 17, 18, 19, 20,

21, 22, 23, 24, 25, 26, 27, 28,

29, 30, 31, 32, 33, 34, 35,

36, 37, 38, 39, 40, 41, 42, 43,

44, 45, 46, 47, 48, 49, 50,

51, 52, 53, 54, 55, 56, 57, 58,

59, 60, 61, 62, 63, 64, 65,

66, 67, 68, 69, 70, 71, 72, 73,

74, 75, 76, 77, 78, 79, 80,

81, 82, 83, 84, 85, 86, 87, 88,

89, 90, 91, 92, 93, 94, 95,

96, 97, 98, 99, 100, 101, 102, 103, 104,

105, 106, 107, 108, 109, 110, 111, 112, 113,

114, 115, 116, 117, 118, 119, 120 121, 122, 123,

124, 125, 126, 127, 128, 129, 130, 131, 132,

133, 134, 135, 136, 137, 138, 139, 140, 141,

142, 143, 144, 145, 146, 147, 148, 149, 150, 151,

152, 153, 154, 155, 156, 157, 158, 158, 159,

160, 161, 162, 163, 164, 165, 166, 167, 168,

169 . . .

1, 2, 3, 4, 5, 6,

7, 8, 9, 10, 11, 12, 13,

14, 15, 16, 17, 18, 19, 20,

21, 22, 23, 24, 25, 26, 27, 28,

29, 30, 31, 32, 33, 34, 35,

36, 37, 38, 39, 40, 41, 42, 43,

44, 45, 46, 47, 48, 49, 50,

51, 52, 53, 54, 55, 56, 57, 58,

59, 60, 61, 62, 63, 64, 65,

66, 67, 68, 69, 70, 71, 72, 73,

74, 75, 76, 77, 78, 79, 80,

81, 82, 83, 84, 85, 86, 87, 88,

89, 90, 91, 92, 93, 94, 95,

96, 97, 98, 99, 100, 101, 102, 103, 104,

105, 106, 107, 108, 109, 110, 111, 112, 113,

114, 115, 116, 117, 118, 119, 120 121, 122, 123,

124, 125, 126, 127, 128, 129, 130, 131, 132,

133, 134, 135, 136, 137, 138, 139, 140, 141,

142, 143, 144, 145, 146, 147, 148, 149, 150, 151,

152, 153, 154, 155, 156, 157, 158, 158, 159,

160, 161, 162, 163, 164, 165, 166, 167, 168,

169 . . .

The rest of these numbers are NOT perfect squares.

Why arent the rest of these numbers perfect

squares?

So lets take the number 19

Given 19 square units, lets see if we can build

a square.

19 is a prime number, so we are limited to a 19 x

1 or a 1 x 19 rectangle.

We have enough units to build a 4 x 4 rectangle,

however.

Are we closer to building the 5 x 5, or did we

just barely have enough for the 4 x 4?

And we have these three square units left over.

Estimating Square Roots

With 19 square units, we had enough to build the

4 x 4 square, but not enough to build the 5 x 5

square.

Only 3 left over.

The 4 x 4 square equals 16 square units,

and the 5 x 5 square equals 25 square units.

QUESTION Is 19 units closer to 16 or 25?

Short 6 units!

Estimating Square Roots

lt 19 lt

16 lt

lt 25

15 16 17 18 19

20 21 22 23 24 25

19 is closer to 16 than it is to 25

Estimating Square Roots

0 1 2 3 4

5 6 7 8

9 10

Since 19 is closer to 16 than 25,

Your Turn!

Name the two perfect squares each number is

between, and then circle the one that is closest

to the number.

1) ___lt 6 lt ___

2) ___lt 20 lt ___

3) ___lt 28 lt ___

3) ___lt 44 lt ___

Answers

Name the two perfect squares each number is

between, and then circle the one that is closest

to the number.

1) 4 lt 6 lt 9

2) 16 lt 20 lt 25

3) 25 lt 28 lt 36

4) 36 lt 44 lt 49

Your Turn!

Name the two perfect squares each number is

between, and then circle the one that is closest

to the number.

5) ___lt 34 lt ___

6) ___lt 17 lt ___

7) ___lt 31 lt ___

8) ___lt 52 lt ___

Answers

Name the two perfect squares each number is

between, and then circle the one that is closest

to the number.

5) 25 lt 34 lt 36

6) 16 lt 17 lt 25

7) 25 lt 31 lt 36

8) 49 lt 52 lt 64

Your Turn! Each SQUARE ROOT is

between two integers.

Name the integers, and then circle the best

estimate for the square root of the given number.

Your Turn! Each SQUARE ROOT is

between two integers.

Name the integers, and then circle the best

estimate for the square root of the given number.

Answers Each SQUARE ROOT is between

two integers.

Name the integers, and then circle the best

estimate for the square root of the given number.

4 9

16 25

25 36

36 49

Answers Each SQUARE ROOT is between

two integers.

Name the integers, and then circle the best

estimate for the square root of the given number.

25 36

16 25

25 36

49 64

Extended Response

Problem You are given 18 square units and asked

to build a square.

- How many of the square units would be necessary

to build a - complete square?

- If you could borrow more square units, how many

square units would you need in total to be able

to build the next larger square?

C) What is the best estimate for the measure of

one side of a square with an area of 18 square

units?

Extended Response

Problem You are given 18 square units and asked

to build a square.

- How many of the square units would be necessary

to build a - complete square?

- Given 18 square units, it would
- take 16 of them (4 x 4 42 16) to build

a complete square, with 3 left over.

4

4

Extended Response

Problem You are given 18 square units and asked

to build a square.

- If you could borrow more square units, how many

square units would you need in total to be able

to build the next larger square?

B) With more square units, it would be possible

to build a 5 x 5 52 25 unit square. It would

require 6 more square units.

5

5

Extended Response

Problem You are given 18 square units and asked

to build a square.

C) What is the best estimate for the measure of

one side of a square with an area of 18 square

units?

4

C) Since 18 is closer in value to 16 than it is

to 25, the side of a square with an area of 18

square units is approximately equal to the square

root of 16 which is 4. (v18 4)

16

4

5

25

5

Extended Response

- Since 18 is closer in value to 16 than it is to

25, the side of a square with an area of 18

square units is approximately equal to the square

root of 16 which is 4. - (v18 4)

C) What is the best estimate for the measure of

one side of a square with an area of 18 square

units?

4

15 16 17 18 19 20 21 22

23 24 25

16

4

5

v18

v16

v25

25

0 1 2

3 4 5

5

Calculator Exercises

Use your calculator to find the following square

roots. Round answers to the nearest tenth.

1) v14

2) v42

3) v21

4) v47

5) v58

6) v60

7) v35

8) v75

9) v66

10) v55

11) v67

12) v80

Calculator Exercises

Use your estimates to find the following square

roots rounded to the nearest whole number.

9 16

36 49

16 25

36 49

1) v14

2) v42

3) v21

4) v47

3.7

6.5

4.6

6.9

4

7

5

7

49 64

49 64

25 36

64 81

5) v58

6) v60

7) v35

8) v75

7.6

7.7

5.9

8.7

8

8

6

9

64 81

49 64

64 81

64 81

9) v66

10) v55

11) v67

12) v80

8.1

7.4

8.2

8.9

8

7

8

9

Are you an expert now?

Just look at all those squares!

You will need to be for the Pythagorean Theorem!

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Home About Us Terms and Conditions Privacy Policy Presentation Removal Request Contact Us Send Us Feedback

Copyright 2018 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2018 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Squares" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!