Patrick's Textbook Post Pages 103-105. Numbers 5,8,11,14

area of square = a²
area of square = 6x6
area of square = 36cm²

area of square = b²
area of square = 8x8
area of square = 64cm²

a² + b² = c²
6² + 8² = c²

36 + 64 = c²
100cm² = c²



√100cm² = √c²
10cm = c

a² + b² = c²

50² + 200² = c²
2500 + 40 000 = c²
42500 cm² = c²
√42500 cm² = √c²

206 cm = c

√914 = √c²
30.2 cm = c

c² - a² = b²
30.2² - 17² = b²
912 - 289 = b²
623 cm² = b²
√623 cm² = √b²

25 cm = b

perimeter = a + b + c
perimeter = 17 + 25 + 30.2
perimeter = 72.2

b²=c²-a²
b²=5²-3²
b²=25-9
b²=16m²
√b²=√16m²
b=4m

c²=a²+b²
c²=6²+4²
c²=36+16
c²=52m²
√c²=√52m²
c=7.2m
The length of c is 7.2m.

a. Identify a whole number with a square root between 2 and 9

√64 √75 √81
8 8.something 9

b.How many whole numbers can you find that have a square root between 8 and 9?Show your work.

665,66,67,68,69,70,71,72,73,74,75,76,7,78,79,80

Show You Know

For each of the following, use perfect square to estimate the square root to one decimal place. Check your answer with a calculator.

√18
4 Square
5 Square
4. 25

√23
4 Square
5 Square
5.8

√35
5 Square
6 Square
6.9

Scribe 3 Show You Know Page 84 Page 85 Questions 3,7,12,14

Show You Know, Page 84.
Determine the side length of a square with an area of 196cm².

||||||196cm²
||||||/||||||||||\
||||14|||X|||14
|||/|||\|||||||||/||||\
||7 x 2 |x| 7 x 2

196=7x2x7x2
196=14x14
√196=14
The side length is 14cm.

Page 85 Questions 3,7,12 and 14.

Question 3:
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Use words and/or diagrams to explain how you know which factor is the square root of 36.

|||||36
|||/|||||||\
||6||X|||||6
/||||\|||||||/||||\
3 x 2 X 3 x 2

36=3x2x3x2
36=6x6
√36=6
The square root of 36 is 6.

Question 7:
Write the prime factorization of each number. Identify the perfect squares.

A)||||||42
||||||/||||||||\
||||7 |||x||| 6
||||||||||||||/||||\
||||7|||x|3||x||2
This is not a perfect square.

B)||||||169
|||||||/|||||||\
||||||13 |x| 13
This is a perfect square.

C)|||||||256
|||||||/|||||||||||\
|||||16|||X||||||16
|||/|||||\|||||||||/|||||||||\
||4||x||4|x||||||4||x||||4
/|||\|||||/|||\|||||/|||\|||||/|||\
2x2 x 2x2 x 2x2 x 2x2
This is a perfect square.

Question 12:
Determine the square of each number.

A)SxS=Area
||10x10=100

B)SxS=Area
||16x16=256

Question 14:
Determine the side length of a square with an area of 900cm²

√900=30.

Question 17:
A fridge magnet has an area of 54mm². Is 54 a perfect square? Use prime factorization to find the answer.

||||||||54mm²
|||||||/|||||||||\
|||||27|||||x|||2
|||/||||\
||9||x||3|||x|||2
/||||||\||||||||||||||
3 x 3|x|3|||x|||2

It is not a perfect square.

Glenesse's Scribe 2

Show You Know pg. 83, pg. 85 Question 2, 6, 11, 15.

Show You Know pg. 83

Question:

Determine the area of a square with a side length of 16mm.

Answer:

We all know that a square has 4 equal sides so you multiply the side length of 16mm by itself.

16x16=256 mm squared

The area of the square that has a side length of 16mm is 256 mm squared.

Page 85

Question:

2)How would you use prime factorization to determine the square root of 225? Compare your answer with a classmate's.

Answer:

So 225 is a perfect square.

After you compare it to your classmate's

Question:

6)A rectangle has an area of 64 m squared

a)Determine the prime factorization of 64.

b)Is 64 a perfect square? Explain.

c)Draw a square with that area and label its side length.

Answer:

a)

b) 64 is a perfect square because the prime factor is 2 and it can be divided into equal parts.

c)

Question:

11)What is the area of a square with each side length?

a) 10

b) 16

Answer:

a) 9 x 9 = 81 unit squared

b) 16 x 16 = 121 unit squared

Question:

15) Evaluate

a) 49 squared

b) 64 squared

c) 625 squared

Answer:

I used a calculator for this question.

a) 49 squared = 7

b) 64 squared = 8

c) 625 squared = 25

Here is a site to help you with prime factorization.

Square Number and Square Roots

Last Thursday's Lesson (:

Focus on...
Determine the square number of a whole number.
Determine the square root of a perfect square.

A Square Number is the product of the same two number.
Example : 3 x 3 = 9, so 9 is a square number

A square number is also known as a perfect square.

Perfect Squares are
1, 4, 9, 16 and etc...

Don't forget today homework!

Start a number line on the other crease on
the bottom and highlight the perfect square numbers.

Estimatating using perfect squares, prime factorization and number line

Homework from yesterday
- Estimating using perfect squares


200- in between the perfect squares 196 and 225.
- 225 is bigger than 200 so that number won't work
- so that leaves us with 196 aka 14x14
- If 196 is 14x14 that means that 200 will be 14._x14._=200 because we know that 225 which
Is to big being 15x15 or the next highest perfect square.

37-in between perfect squares 36 and 49
- 49 is bigger than 37 so it won't work
- which leaves us with 36 aka 6x6
- so if 36 is 6x6 that means that 37 will be 6._x6._=37 because we know that 37 which
to big being 7x7 or the next highest perfect square

850- in between perfect squares 841 and 900
- 900 is bigger than 850 so it won't work
- which leaves us with 841 aka 29x29
- so if 841 is 29x29 that means that 850 will be 29._x29._=850 because we know that 900 is
to big being 30x30 or the next highest perfect square

77 - in between perfect squares 64 and 81
- 81 is bigger than 77 so it won't work
- which leaves us with 64 aka 7x7
- so if 64 is 7x7 that means that 77 will be 7._x7._=77 because we know that 81 is
to big being 8x8 or the next highest perfect square

Number Line

-1-25
-Different colours for the pefect squares
-show what x what = the number your trying to get to

Im sorry my computer won't let me put pictures or vidoes.

so heres a link for a Prime Factorization video.
and another link for prime factorization which is a website which has pictures
and then here is my actual link (make sure to turn off the volume if the play the game)

Square Root

Square Root is an inverse of squaring:
The square root of 25 is SxS or what times itself has a product of 25. 5x5=25

Finding the square root using a calculator:

We also learned how to find the square root of a number. From what I've learned so far the only real way to get the square root of a number is to use your trusty old calculator. Of course, each calculator is different, so you may have to punch in a few things before you get the answer.

Let's take the number 3. I know what you're thinking, "but, it's impossible to make a square out of that!" If you remember from last class, it is possible, just a lot less simple to find. So, that's where square root comes in.

Okay then, now punch in the square root function on your calculator and you should get: 1.414213562. Well, that's not a nice number to work with, so let's just take the numbers up to the thousandths place, no rounding please. So, now we should have 1.41.
1.41 x 1.41=1.9881
Not exactly a perfect square, but it's close.

Estimating the square root using fractions:

Remember the number line we made for homework? That would come in handy right about now.


As you can see the space between the two perfect squares is divided into 3. So then we will be using 3 as the denominator for the following fractions. It won't be as exact as the calculator, but it's close.
1: 1
2: 1 1/3
3: 1 2/3
4: 1 3/3 or 2
See how that works? Remember, we won't just use 3 as the denominator. For example the next fraction should be out of 5, since the space between the 2nd perfect square and the 3rd perfect square is divided into 5.

Estimating the square root using perfect squares:

Either the number line or the chart we did would be useful for this activity.

First let's take a number like, 439, and find the square root. Now don't panic, it's a lot easier than you think.
Find on the chart 2 numbers where 439 falls between. It should be 400 and 441.
Next we look on our chart to find the square root or side lengths of both numbers, which would be, 20 and 21. This means the square root of 439 would lie between 20 and 21.
The number can't be 20 or 21 so it should be 1 of those two numbers and a decimal. But which number should be used? 20 of course! If you used 21 and a decimal it would no longer be a number in between the two.
So the answer is 20.___ You don't need the rest, this is an estimation after all.

Now that you know this the homework shouldn't be much of a problem.

Homework:

Use fractions to estimate the square roots of 1-25.
Use perfect squares to estimate the square roots of 200, 37, 850, and 77.

If you're still having trouble with this, here is a site I think you should look at. This probably isn't the best site out there, so leave links to other sites in the comments section and I'll be sure to change it.
Also, here is a video. Also not the best video, so a link or two to another one would be just great.