# Thread: Challenge: can you find the square root of n using only one of the 4 operations?

1. Here is a nice challenge for math lovers:

can you work out an algorithm that uses only one operation [sign] + - : x , (excluding log, and sqrt) to find the square root of any number ?
You are allowed to use your mind for preliminary 2-digit basic operations (times table , 8 +/- 3....and so on).

It is not tough!  2.

3. Suppose I'll express this as which implies that is . So all I used was multiplication That's my "algorithm". LoL.

(can you elaborate on what you're asking?)   4. Originally Posted by brody (can you elaborate on what you're asking?) You can find on wiki the known algorithms to take a sqrt  5. b-b=a?  6. Originally Posted by incorrect b-b=a?
That is incorrect, incorrect You have to define what "a" and "b" are to represent otherwise your proof/algorithm makes no sense.  7. Originally Posted by logic  Originally Posted by brody (can you elaborate on what you're asking?) You can find on wiki the known algorithms to take a sqrt
I'm assuming it's this "Babylonian method". (???) Originally Posted by Wikipedia: Square root
The most common iterative method of square root calculation by hand is known as the "Babylonian method" or "Heron's method" after the first-century Greek philosopher Heron of Alexandria...
I think I understand it. See if this is right. I'll use as an example. . I know that . Therefore .

So the average of and should yield a closer value to .

So now I'll take this closer value, here being which I know is greater than , divide it from 2 and average that value to get an even closer approximation to . However, I don't think you can get the exact value without infinite iteration. And I'm sure the math and the numbers will get really nasty as the process goes deeper! (after all, it's approaching an irrational value)

Interesting!  8. b squared + a squared =c squared . find the square root of c  9. Originally Posted by brody I'm assuming it's this "Babylonian method". (???)
To my mind, that doesn't meet the requirements as it needs two operations (division and subtraction). Unless you "cheat" and say that comparison isn't "really" an operation. But that means you never write a program to do it.   10. You can approximate it to any degree by doing this:

To find √n

Starting at 1, try all the natural numbers in order until you reach the greatest such that k is then the whole number part of the answer.

To find the first decimal digit try squaring k.0, k.1, k.2, ... k.9 in order until you find the greatest such that To find the second decimal digit repeat the same process with instead of Etc.

I hope that kind of makes sense.

I don't think you can find a non approximation algorithm though.  11. Originally Posted by brody
, I don't think you can get the exact value without infinite iteration. And I'm sure the math and the numbers will get really nasty as the process goes deeper! (after all, it's approaching an irrational value)....Interesting!
You cannot get that with any method, brody, of course you must take a finite number x, say to a 10-digit accuracy. (Wiki chooses 6-digit precision).

Now, only one operation is surely possible and is +, or - : addition or subtraction of the gnomons , odd numbers
the problem is that it is too expensive: for n = x² it requires x operations
The challenge is more sophisticate, asks for a solution less expensive than Newton's (20 operations) and Babylonian's (15)
I assure you it is possible, not too tough!  12. Finding Square Roots arallel-method. Worteltrekken via parallel berekening. - YouTube
I think this guy found a solution for the roots, he write that the red numbers are not a accidental, maybe right or not?  13. If you are saying 'any' number i.e choose our own number then yes fairly easy, if by any you really mean every then that's harder. Some guidance on what you mean would be helpful regarding this.  Bookmarks
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