Wednesday, January 11, 2012

Some more Squaring Work

Here are a few questions.  Try them out and see if they improve your test score on Thursday's quiz.
Feel free to leave answers as a comment! :)

1. Use prime factorization to show whether 120 and 196 are perfect squares?

2. What is the area of  a square picture with a side length of 22cm?

3. Challenge yourself to memorize the perfect square numbers from 1 to 225.  Can you repeat them from lowest to highest and then back down to lowest in under 1 minute? Bonus mark on the quiz if you can do this!

4. Determine which of the following numbers are perfect squares: 10, 100, 1000, 10 000, 100 000.
a) State the square root of each perfect square.
b)How do you know that the others are not perfect squares?
c)Create a quick method for determining mentally if the numbers are perfect squares.
d)Use this method to determine if 1 000 000 000 is a perfect square.

5. Determine the square root of 6400, 640 000, 64 000 000.
a) Describe a quick method for determining mentally the square root each number above.
b) Explain why this method does not work for evaluating the square root of 640.
What is the square toot of 640 000 000 000. How did you find your answer.

15 comments:

Mr. H said...

816 is thebest room

devonr816 said...

I did the work and im wondering if for question 2. the answer is 11x2 haha just double checking XD

gerard816 said...

1. 120 is not a perfect square but 196 is a perfect square.
2. The area of a square picture with a side length of 22cm is 484 cm*.
4. Square root of 100 is 10 and the square toot of 10000 is 100. b) The others are not perfect squares because their prime factorization doesn,t have a set of factors that is the same value as the whole number given. c) The number of zeros had to be even. d) 1 billion is not a perfect square.
5. Square root of 6400 is 80, 640000 is 800, 64000000 is 8000. a)Find the square root of 64 which is 8 then write half of how many zeros there were. b) It's not a perfect square.
The square root of 640 000 000 is 800 000. With the method I used on 5a).

kim873 said...

1. Use prime factorization to show whether 120 and 196 are perfect squares?

120 is not a perfect square because the closest number you can get is 121 if you multiply 11 x 11. But since there is not squared numbers to equal 120, I used 60 x 2= 120. from 60, I got the prime factors for that to get 30 x 2. (60 ÷ 2 = 30) Then I knew that to make 30 you multiply 3 x 10, and then divided 2 from the 10 to get 5. The bottom branches would be 5 x 2. But you also have to add the Line of Factorization so it would be 5 x 2 x 2 x 2 x 3. If you would basket the numbers and separate them so that both groups could have an even pair of numbers, both groups wouldn't get an equal share.

196 is a perfect square because I know that 14 is a number that can be multiplied by itself to get the answer of 196, so it would be 14 x 14. From there you divide it so the next branches would be 7 x 2. Your Line of Factorization would be 7 x 2 x 7 x 2. Both sets of baskets would have an equal share.


2. What is the area of a square picture with a side length of 22cm?

The area of a square with a side length of 22cm would be 484cm2<<< exponent symbol since it is about area.

4. Determine which of the following numbers are perfect squares: 10, 100, 1000, 10 000, 100 000.

a)
-Square root of 100 = 10
-Square root of 10 000 = 100
-Square root of 100 000 = 10 0000
b)
-I know that the others are not perfect squares because the square root of 10 = 3.16227766, and the square root of 1000 = 31.6227766. Square numbers are only supposed to be whole numbers multiplied by the same whole number to get your answer.

5. Determine the square root of 6400, 640 000, 64 000 000.

-Square root of 6 400 = 80
-Square root of 640 000 = 800
-Square root of 64 000 000 = 8000

a)
-You take the zero's from the number you are going to square root and for your answers it would be half the amount of zero's from the square root number.
EX: square root of 64 equals 8. That means the square root of 6 400 would be 80 because half of 2 equals 1, so you get 1 zero.
b)
640 only has one zero, so it is impossible to have your answer as 640 if the square root of 64 = 8 and the square root of 6 400 = 80. The number would have to have a decimal because the real answer for the square root of 640 = 25.29.

6. What is the square root of 640 000 000 000. How did you find your answer.

Square root of 640 000 000 000 = 800 000 with the method I used in 5 a).

Jennifer873 said...

1. 120 is not a perfect square because I found the prime factors: (2x3x2x5x2) This can't be seperated so each side won't be balanced. 196 is perfect square because I know 14 is a prime number that you muliple itself to get to 196. If you go 14x14 it will lead you to 7x2 on both sides. So now I know it's a perfect square.

2. The area of a square that has 22cm as a side length is 484cm^ <- (exponent. I used the formula side x side= area. So 22cm x 22cm is 484cm^.

4. 100, 10 000 are perfect squares
a) Square root of 100- 10
Square root of 10 000- 100

b)The other numbers are not perfect squares because there isn't a whole number that can be multiplied by itself to get numbers such as 10, 1000,
100 000.

c) Every number must have even numbered zeros.
d) 1 000 000 000 is not a perfect square, this is because there isn't an even amount of zeros.

5. 6400- 80
640 000- 800
64 000 000- 8000

a)You know that 8x8 is 64 so 8 is a key number. Now if there is an even amount of zeros, seperate them into 2 groups. Take the number 8 and put it with the amount of zeros in one group and put the zeros in there original place with the number 8. If you have 2 groups of the same number, you found the square root for it.

b)There is not a even amount of zeros so that's why this method does not work.

The square root of 640 000 000 000 is 800 000. I found my answer using the method I have recently used to fine 5a).

kim873 said...

4.
c)
The numbers had to be an even amount of pairs to share equally among the two baskets.

Priya873 said...

1. 120 = 10.95445115
196 = 14

196 is a perfect square and 120 is not a perfect square.

2. The area of a square picture with a side length of 22 cm is 484 square cm. Because 22 x 22 = 484

3. 1,4,9,16,25,36,49,64,81,100,121,144.

4. 100 and 10 000 are both perfect squares. 10, 1000 and 100000 are not perfect squares.

a. What I did was I punched in the square root button that's on my calculator then punched in the number like 1000 and it equaled 10. 10 is a perfect square.

b. Because the numbers aren't whole numbers.
Ex. 31.6227766.

c. If the number of zeros are even.

d. 1 000 000 000 is not a perfect square. The reason why is because on my calculator I punched in the square root button and punched in 1 000 000 000 and the answer was 31622.7766, which is not a perfect square.


5.
6400 = 80
640 000= 800
64 000 000= 8000
They are all perfect squares.
a. I punched on my calculator the square root button then 6400 which equaled 80. And I did the same with the other numbers.

b. Because 640 is not a perfect square.

c. The square root of 640 000 000 000 is 800000. I punched the square root button on my calculator then 64 000 000 000 and it equaled 800000.

hannah816 said...
This comment has been removed by the author.
hannah816 said...

1. 120 is not a perfect square. Prime factorization of 120 is 3x2x2x5x2. 196 is a perfect square. Prime factorization of 196 is 7x7x7x7.

2. The area of a square picture with a side length of 22cm is 484cm2 <exponent

4. 100, 10 000, 100 000 are perfect squares.
a) square root of 100 is 10
square root of 10 000 is 100
square root of 100 000 is 10 000
b) I know that the others are not perfect squares because the square root of the others are not whole numbers.
c) An even number of zero will be a perfect square.
d) 1 billion is not a perfect square because it has an odd number of zeros.

5 square root of 6400 is 80
square root of 640 000 is 800
square root of 640 00 000 is 8000
a)Take the square root of 64, which is 8, then attach half of the number of zeros from the original number to 8.
b) There isn't an even number of zero in 640, therefore the method does not work.

The square root of 640 000 000 000 is 800000.I found my answer using the method in 5a) ; square root if 64 is 8 there is 10 trailing of zeros in the original number, attach half of the number of zeros, which is 5, to 8.

daphne873 said...

1.) Use prime factorization to show whether 120 and 196 are perfect squares?
*120 is not a perfect square because when you have done Prime Factorization; 120, 60x2, 6x10x2, and the last part had "2x3x2x5x2" and that didn't have an equal amount of numbers to share for the two baskets, and that's why 120 is not a perfect square.
*196 is a perfect square because I already knew that 14x14 equals to 196. But if you did Prime Factorization, you would have 196, 14x14, and 7x2x7x2, and that ends up with 14 x 14, therefore 196 is a perfect square.

2.) What is the area of a square picture with a side length of 22cm?
*To get the area of a square, you need to multiply side x side. SxS=Area, or 22 x 22= 484cm²

4.) Determine which of the following numbers are perfect squares: 10, 100, 1000, 10 000, 100 000.

a) State the square root of each perfect square.
100, 10 000 are perfect squares
-Square root of 100- 10
-Square root of 10 000- 100

b)How do you know that the others are not perfect squares?
*I know that the others aren't perfect squares because when you try to find out their square roots, you always end up with numbers with decimals, and whenever you're finding out perfect squares, you have to have a whole number.

c)Create a quick method for determining mentally if the numbers are perfect squares.
*If you use Prime factorization, you always have to have an equal amount of numbers to be shared for each baskets for you to have a perfect square.

d)Use this method to determine if 1 000 000 000 is a perfect square. 1 000 000 000 is not a perfect square because its square root is 31622.7766, and there isn't an equal amount of zeros for that number, therefore 1 000 000 000 is not a perfect square.

5. Determine the square root of 6400, 640 000, 64 000 000.
*
-Square root of 6 400 = 80
-Square root of 640 000 = 800
-Square root of 64 000 000 = 8000

a) Describe a quick method for determining mentally the square root each number above.
*The number 8 and the number 64, are somehow connected, because 8x8=64, and that would give you some hints on how to answer the next question, and also the amount of zero's are also helpful, I have noticed that half the amount of the place values are also the amount that your answer has. for example,
6 400 = 80, 6 400, as you know have 4 place values, and the square root is 80, which has 2.

b) Explain why this method does not work for evaluating the square root of 640.
*Because there isn't an even amount of zero's or place values. So, it's impossible to have one and a half place value as their square root.

*What is the square root of 640 000 000 000. How did you find your answer. 800 000. Because we already know that 640 000 000 000, has 12 place values, and the square root of it has to have 6. And I remembered that 64 and 8 are somehow connected. So my answer was
800 000.

Jomel816 said...

1. 120: 60-2
6 10 2
3 2 5 2 2
perfect square (196): 14-14
7 2 7 2

2. 22cm²= 484cm

4.a)10(100),100(10000)
b)I used a prime factorization for each number
c)if there is an even amount of zeros it is a perfect square
d)no there is an odd amount of zeros(9)

5. a)what I did was I thought of the number 8 and then for each zero from what numbers u said i add half of the zeros to 8 so 6400 has 2 zeros so I half it which leaves me with 1 zero so i add it to 8 which is now 80
b)there is odd number of zeros
c)800000, there is 10 zeros so it is 5 and then i add it to 8

serena 814 said...

1) 120 is not a perfect square because the prime factors are 3x2x2x5x2.. 196 is a perfect square because the prime factors are both 14. (14x14=196)

2)The area of a square picture with the side length of 22cm is 484cm*. (22x22= 484cm*)

4)10, 1000, 100 000 are not perfect squares because the number of zeros are not even.. 100 and 10 000 are perfect squares because they have an even amount of zeros.
4a) The square root of 100 is 10 (10x10=100)
The square root of 10 000 is 100 (100x100=10 000)
4b) The others are not perfect squares because they don't have an even amount of zeros..
4c) Count the number of zeros, if they are even then the are a perfect square..
4d) 1 000 000 000 is not a perfect square because there are an odd number of zeros..

5)
square root of 6400 is 80
square root of 640 000 is 800
square root of 64000000 is 8000
5a) If you take away the zeros the square root of 64 is 8. Then, add the number of place values to the 8.
5b) This method doesn't work because there is an odd number of zeros..
The square root of 640 000 000 000 is 800 000. The square root of 64 is 8. There are 10 zeros and half is 5. So, i added 5 place values to 8 which gives me 800 000.

irena814 said...

1.. I used prime factorization to show that 120 and is not a perfect but 196 is. The prime factors for 120 is 3, 2, 3, 5, 2 and they can't be equally separated. SO that's why it's not a perfect square..

2. The area of a square picture with a side length of 22cm is 484cm*. (22cm x 22cm = 484cm*)

4..
a) 100 and 10 000 are perfect squares. The square root of 100 is 10 and the square root of 10 000 is 100.
b) I know that all of the other numbers aren't perfect squares because they all have an odd number of zeros.
c)A quick way to determine if all of the other numbers are perfect squares is to see if they have even number of zeros.
d) Using that method, I found that 1 000 000 000 is not a perfect square.

5. The square root of 6400 is 80, the square root of 640 000 is 800 and the square root of 64 000 000 is 8 000.
a) A quick method to determine the square root of the numbers above is to first find the square root of the first two numbers. The square root of 64 is 8. Then divide the number of zeros in two. Next, add the place value of the zeros to 8.
b) The reason why it does not work for the number 640 because it has an odd number of zeros..

The square root of 640 000 000 000 is 800 000. The square root of 64 is 8. And there are ten zeros and half is 5. So I add place value of the zeros to 8 which is 800 000.

Marielle 873 said...

1) 120 is not a perfect square because the prime factorization of 120 wouldn't be equal when they are separate into to basket and if you find the square root using calculator, you will see a number with decimals (10.95445115) To be perfect square, the side length has to have a whole number and has to be balance into the basket. Here's how I found. The prime factorization of 120.. I divide 120 by 2, which is equal to 60 , and put 60x2 at the bottom. Then, I knew that 6x10 is equal to 60, so I continued the branch and put 6x10. I also knew the 2x3 is equal to 6 and 2x5 is equal to 10. The last bottom brachial would be 5x2x2x3... It NOT done! I put all the prime numbers together and makes it the Prime Factorization, 2x2x3x2x2x5.

By looking at 196, I already knew that it is perfect square because 196 is included to the perfect square number that I have to memorize. I also knew it's perfect square because the prime factorization of 196 would be equal into two separate group. And by using calculator, 196 squared is 14 (a whole number).

2) The area of a square with a side length of 22cm would be 484m2 (side, 'side length is 22cm' 22x22 is equal to 484m2)

4 a) 100, 1000, 10000 is perfect square.
B) they are squared with whole numbers and the rest aren't.

C) the numbers has to have even pairs when shared into two basket.

5)Square root of 6400-80
Square root of 640 000-800
Square root of 64000000-8000

A)Find square root of 64 (8) and add the half of how many zeros the number have.

B)640 on has 1 zero.* the number has to have even number of zero to be a perfect square

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