Question

help please

Answer 1

Please show your work.

Find the prime factorization of each number under a radical.


\(27 = 3^3\), for example.

Answer 2

um

Answer 3

@ganeshie8

Answer 4

Not good enough. Find the prime factorization of 20. What small set of prime numbers must be multiplied together to achieve 20? You CAN do it!

Answer 5

(1,2,4,5,10,20) i think

Answer 6

4, 10, and 20 are not prime.
I did not ask for the factors of 20. I asked for the Prime Factorization.

The factors of 27 are 1, 3, 9 and 27
The prime factorization of 27 is 3*3*3

Now for 20...

Answer 7

4*4*4*4*4??????

Answer 8

Is 4*4*4*4*4 = 20? No 4+4+4+4+4 = 20 Also 4 is not a prime number.

I'll get you started.
20 = 2*10

See how 2 is a prime number? Do you know what a prime number is?
10, on the other hand is not a prime number. It must be factored more.

20 = 2*10 = 2*______*______ Fill in the blanks.

Answer 9

no idk what a prime number is and i think 2*10*2 i guess idk

Answer 10

So close. 2*10*2 = 40, not 20. Also, 10 is not a prime number.

20 = 2*10 = 2*2*5

You must see this or you cannot solve this problem.

2 is a prime number
5 is a prime number

Two 2s and a 5, multiplied together give 20. 2*2*5 = 20 -- This gives the prime factorization of 20.

Let's move on to 147. Find it's prime factorization.

Of course, all this talk about prime numbers is of no help if you do not know what a prime numer is.

Answer 11

yes it really is

Answer 12

For now, it is sufficient to define a prime number as a number that cannot be factored.

2 is prime. You can rewrite it as 1*2, I suppose, but that doesn't get us anywhere.
3 is prime. You can rewrite it as 1*3, I suppose, but that doesn't get us anywhere.
4 is NOT prime. 4 = 2*2.
5 is prime. You can rewrite it as 1*5, I suppose, but that doesn't get us anywhere.
6 is NOT prime. 6 = 2*3.

Answer 13

so if you can multiply a number by other numbers other than 1 its not a prim number

Answer 14

Pretty much. As long as you are talking about Natural Numbers.
7 - Prime
8 - Not Prime 2*2*2
9 - Not Prime 3*3
10 - Not Prime 2*5
11 - Prime

Are you seeing the idea?

Answer 15

yes but let me make sure
12-not prime6*2 and 4*3
13- prime
14-not prime 7*2
15- prime
16- not prime 8*2
17- prime
right?????

Answer 16

wait 15 is not prime cus 3*5

Answer 17

15 - Not Prime 3*5 - You just missed this one.

Pretty good!

Notice, however, that 12 = 6*2 is a factorization of 12, but not a PRIME factorization. 6 is not prime. Also, 16 = 8*2 is a factorization but not a PRIME factorization. 8 is not a prime number.

For 12, you might do it like this.
12 = 2*6
Hey, 6 is not prime.
12 = 2*6 = 2*(2*3) -- Okay, now everyone is prime.

Answer 18

You beat me to it!! Excellent work!

Answer 19

Okay, are we ready to tackle 147? Find it's Prime Factorization!

Answer 20

i think

Answer 21

First, find ANY factorization. We can worry later about whether or not it is Prime.

Answer 22

You can just start from the bottom.

147 / 2 = Nope. That doesn't work.
147 / 3 = 49!! There it is!

Answer 23

factors(1,3,7,21,49,147)
prime factors(3*7*7) i think

Answer 24

@hughana

Answer 25

@i0iz0gangster

Answer 26

@hobbs978

Answer 27

You have it! Why do you doubt? Now, all the way back to the beginning:

\(\sqrt{5}+\sqrt{20} - \sqrt{27}+\sqrt{147}\)

Rewrite with Prime Factorizations

\(\sqrt{5}+\sqrt{2^{2}\cdot 5} - \sqrt{3^{3}}+\sqrt{3\cdot 7^{2}}\)

After that, it's a matter of pulling out the perfect squares.

\(\sqrt{5}+2\sqrt{5} - 3\sqrt{3}+7\sqrt{3}\)

You have to see what just happened. Give it some thought.