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Is it possible to find √n using only the times table and the 4 operations?
It is possible:Office_Shredder said:Using only finitely many such operations, you cannot...
It depends on what you mean by "find".logics said:Is it possible to find √n using only the times table and the 4 operations?
Reference? I find this claim rather unlikely...TheDestroyer said:That's actually how computers calculate square-roots.
That's actually how computers calculate square-roots.
Hurkyl said:Is it cheating to use the operation "<"?
Office_Shredder said:It's a binary operation, which takes two inputs a<b and returns 1 if a is smaller than b, and 0 otherwise. Hurkyl was noting my tremendous reliance on it in my example despite it not being one of the permissible operations in the original post. I can't figure out a workaround either
When I say can you find x =[itex]\sqrt{635²}[/itex] using only logics I mean using only your mind, knowing by heart the times table, using no calculator, no pencil and paper.Office_Shredder said:logics, if you just want the square root of something you know is an integer you can just use a binary search...
logics said:When I say can you find x =[itex]\sqrt{635²}[/itex] using only logics I mean using only your mind, knowing by heart the times table, using no calculator, no pencil and paper.
Well done, Mentallic, if you can manage all that in your mind!Mentallic said:So [tex](600+10B+5)^2=(600+(10B+5))^2=600^2+1,200(10B+5)+(10B+5)^2[/tex]
Clearly the influence would be that middle term [itex]1,200(10B+5)[/itex]...Thus, ABC = 635
logics said:Well done, Mentallic, if you can manage all that in your mind!
But you must find something simpler if you want to solve the challenge in the twin-thread about the cube root... (try to find x = [itex]\sqrt[3]{723³}[/itex]).
If you do not wish to move on to that thread, here is a slightly tougher [but still easy] challenge: find x = [itex]\sqrt{277729}[/itex]
Practice [or luck] is not needed, only an efficient method, algorithm i.e.: logics.Mentallic said:With a bit of practice, I could answer the square root problems ...a useless skill
And obviously I'd have little luck extending it to the cube roots.
That is a good method, Dickfore, do you know the Bakhshali method? Does it converge faster than Babylon, as wiki hints?Dickfore said:You can find the square root [tex]x_{n + 1} = \frac{1}{2} \, \left( x_n+ \frac{a}{x_n} \right)[/tex] The convergence is fast though,.
Yes, it is possible to find the square root of a number using only basic mathematical operations such as addition, subtraction, division, and multiplication. However, the process may be more complex and time-consuming compared to using a calculator or a specialized square root algorithm.
To find the square root of a number using only basic mathematical operations, you can use the long division method or the repeated subtraction method. Both methods involve trial and error until the desired result is obtained.
The accuracy of finding the square root of a number using only basic mathematical operations depends on the precision of the calculations and the number of decimal places used. With enough iterations and calculations, the result can be accurate, but it may not be as precise as using a calculator or a specialized algorithm.
The limitations of finding the square root of a number using only basic mathematical operations include the complexity and time required for the calculations, as well as the potential for errors. It may also be difficult to find the exact square root of a number with a high number of decimal places using this method.
Finding the square root of a number using only basic mathematical operations can be a helpful exercise in understanding the principles of mathematics and improving mental math skills. It can also be useful in situations where a calculator or specialized algorithm is not available.