Square roots: mathematical way to confirm that 11*33=11^2*3 ...?

[davehogan]

I know that 11*33=11^2*3 because it's in my book and I've confirmed it mathematically. Is there an easy way or formula to work this out?

 

[Deleted member 4993]

I know that 11*33=11^2*3 because it's in my book and I've confirmed it mathematically. Is there an easy way or formula to work this out?

11 * (33) = 11 * (11 * 3) = 11 * 11 * 3 = (11 * 11) * 3 = (11²) * 3 = 11² * 3

 

[pka]

I know that 11*33=11^2*3 because it's in my book and I've confirmed it mathematically. Is there an easy way or formula to work this out?

This is a useful theorem: Any positive integer is the product of powers of primes.
Example: \(\displaystyle A=475,200~\&~B=8575875\)
Now we factor both \(\displaystyle A=2^6\cdot3^2\cdot5^2\cdot11~~\&~~B=3^4\cdot5^3 \cdot 7 \cdot 11^2 \)
One can use this free website to factor. Look Here. You can just change the number and use the \(\displaystyle \boxed{~=~} \).

Now we multiply the two: \(\displaystyle A\cdot B= 2^6\cdot3^6 \cdot5^7 \cdot 7 \cdot11^3 \) We simply add powers of like primes.

 

[lookagain]

This is a useful theorem: Any positive integer is the product of powers of primes.

No, any positive integer is not the product of powers of primes. One is a positive number,
and it is not the powers of primes.





(A rank amateur would claim what is in the quote box.)

 

[Ishuda]

No, any positive integer is not the product of powers of primes. One is a positive number,
and it is not the powers of primes.





(A rank amateur would claim what is in the quote box.)

Hey lookagain,
Look again. What is
2⁰*3⁰*4⁰*5⁰

 

[lookagain]

Hey lookagain,
Look again. What is
2⁰*3⁰*4⁰*5⁰

That doesn't work.

"In mathematics, a prime power is a positive integer power of a single prime number.
For example: 5 = 5¹, 9 = 3² and 16 = 2⁴ are prime powers, while 6 = 2 × 3, 15 = 3 × 5
and 36 = 6² = 2² × 3² are not. The number one is not counted as a prime power."


Source:

https://en.wikipedia.org/wiki/Prime_power

 

[pka]

That doesn't work.

"In mathematics, a prime power is a positive integer power of a single prime number.
For example: 5 = 5¹, 9 = 3² and 16 = 2⁴ are prime powers, while 6 = 2 × 3, 15 = 3 × 5
and 36 = 6² = 2² × 3² are not. The number one is not counted as a prime power."


Source:

https://en.wikipedia.org/wiki/Prime_power

PRIME FACTORS. done by Stephen Wolfram

 

[davehogan]

Thanks

Many thanks. I can see I'll have to brush up on my factoring.