POTW #18 is below:
Thursday, January 14, 2016
POTW #18 - Prime Picking
Great work on POTW #17. I liked seeing the full responses out of some people. Make sure you always provide details in your answers! The total area to carpet was 24,000cm squared and the total area to paint would be 18,000cm squared. Does anyone know what these measurements would be in meters squared?
POTW #18 is below:
POTW #18 is below:
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Using the smallest prime numbers; 2, 3, and 5
ReplyDeleteNow to multiply them together
2(4) x 3(9) x 5(25) = 900
(2 x 3 x 5)2 = 900units2
900 units2 = 30 by 30 square
The smallest perfect square numbers include 9, 16, 25, 36, which are squares of 3,4,5,6 in that order.
ReplyDelete9's only factors are 3, 1,9
16 is dividable by 1,8,2,16,3,6,4
25 is dividable by 1,25,5,
36 is dividable by 1,35,2,13,3,etc (it doesn't matter since there are already 3 prime numbers on this list. 2,3,13)
Therefore 36 is the smallest perfect square with 3 prime factors.
wait wait wait...
Deletei completely messed up.
Attempt 2
36 doesn't work
The smallest primes are 2, 3, 5
so if you multiply those with each other and square the outcome, it should produce the smallest square.
(2*3*5)2= 30
30*30=900.
Ok New answer is 900cm2 is a perfect square with 3 prime factors
Because the perfect square has to have 3 prime numbers as its factors, I chose the three smallest prime numbers, 2, 3, and 5. Then, I multiplied their squares, 4, 9, and 25 together, to get 900. Therefore, 900 is the smallest perfect square. It can be found by doing 30 x 30, or 30 squared.
ReplyDeleteWe can do this by simply finding the smallest prime numbers, here are some from 2: 2,3,5,7,11. We know that the three smallest from these numbers are 2,3 and 5. When we multiply this, we get 30:
ReplyDelete(2x3)x5=6x5= 30.
We need to square this to to obtain the smallest perfect square, which is 900.
So after trying out a bunch of numbers I decided to find the smallest prime numbers (2,3,5) and square them so it is 4,9 and 25. Then I multiplied them and got 900 (30x30)and since I know that this number is a perfect square I decided to use this number as the smallest perfect square that has 3 prime numbers as its factors.
ReplyDeleteA prime number is a number that can only be divided by 1 and itself. The smallest prime number would be 2,3,5 which if multiply, you get 30. Now you have to "square" the number or change the dimension which will get 900 as 30 by 30 equals 900
ReplyDeleteThe answer is 900. To get the smallest possible number, I had to find the smallest possible prime numbers. I know 2, 3 and 5 are the smallest prime numbers. To find the common factor, I multiplied them together to get 30. Since I need to find the perfect square, I squared 30, or multiplied by itself. I got 900.
ReplyDeleteI first found the smallest prime numbers: 2, 3, 5 then multiplied them by each other: 2x3x5=30. Then 30x30=900 making the smallest perfect square with 3 prime numbers as factors, 900 squared.
ReplyDeleteFirst I found the smallest prime numbers, which would be: 2, 3, and 5. I multiplied those together: 2(2*3*5) = 30. Square that: 30*30 = 900. Therefore, the smallest perfect square would be 900.
ReplyDeleteThe smallest prime numbers are 2,3 and 5. They are only divisible by 1 and themselves and are greater than 1. When multiplied, they equal 30. 2x3x5 -> 6x5 = 30 To get a perfect square, we need to multiply 30 by itself. 30x30 = 900 Therefore, 900 is the smallest perfect square with 3 prime numbers (2,3 and 5).
ReplyDeleteI don't understand this question at all...
ReplyDeleteLook at some of your peer's work for inspiration Renee.
DeleteI did, but I still don't understand what the question is asking...
DeleteI saw other people's work, but I don't understand why they did it. I don't understand past the choosing the smallest prime numbers (2,3,5)
DeleteNever mind, I got it now...
DeleteMultiply the three smallest prime numbers to get the smallest perfect square. Those are 2, 3, and 5. 2 * 3 = 6 * 5= 30. then square that to get the perfect square of 30. 30 * 30 = 900. the smallest perfect square with 3 different prime factors is 30 squared or 900.
ReplyDeleteI did mine hard copy...
ReplyDeleteTo find the answer to this question you first have to take the smallest prime numbers,then find the squares of all them(I might have made squares a word in this response) and multiply them together. The smallest prime numbers are 2,3,and 5. The squares of all these numbers are 4,9 and 25. 4x9=36,36x25=900. The smallest perfect square possible is a 30x30 square.
ReplyDeleteThe smallest prime numbers are 2, 3, and 5. Then you square those numbers.
ReplyDelete2x2=4
3x3=9
5x5=25
Then I multiplied 25x9x4 to get 900 which is equal to 30x30. A perfect square.
Wait my first answer could or could not be wrong I am not sure. The LCM of the smallest possible prime factors is not 30. It's 18. So the correct answer would be an 18x18 square. P.S correct me if I'm wrong.
ReplyDeleteNevermind I forgot it was 2,3,5 not 2,3,9. whoops
ReplyDeleteTo get the smallest perfect square using prime numbers, then you must choose the smallest prime numbers: 2,3, and 5
ReplyDeleteNow, looking at the example, I understood that you would multiply the prime numbers by each other: 2 X 3 X 5 = 30
So each side of the square would be 30 units.
So the smallest perfect square would be 30 by 30, or 900 units squared.
To get the smallest square you need the smallest prime number, which are 2, 3, and 5 so if I multiply their squares (4, 9, 25) you get 900 so the smallest perfect square made from 3 prime factor is 900 units squared.
ReplyDelete