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logics
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what is the quickest way to find [itex]\sqrt[3]{n}[/itex] [on a pocket calculator] whitout using any [itex]\sqrt{}[/itex] or log key?
HallsofIvy said:Now use 'Newton's algorithm" to solve that equation-...
logics said:how long does that take to find the cube root of a 30-digit number, [on a 10-digit-display calculator] ?
isn't there any better and simpler way?
scurty said:Here is the formula you should use on your calculator. Type in your starting number and press the Enter button. Now type in (using Hall's formula):...
logics said:....without using a pencil. Is that trick generally known?
can you find x = [itex]\sqrt[3]{377933067}[/itex] using only logics, knowing that n = x³ ?
TheDestroyer said:
logics said:what is the quickest way to find [itex]\sqrt[3]{n}[/itex]
Newton's method requires 7 operations per round : [(2 * x * x * x) - a] : (3 * x * x)HallsofIvy said:[tex]x_{n+1}= x_n- \frac{x_n^3- a}{3x_n^2}= \frac{2x_n^3- a}{3x_n^2}[/tex]
Why start with such a huge number?, if a is 377933067 a/3 is 125,977,689. Starting with this x0, it takes 38 rounds to get x, which means 266 operations!The starting value, [itex]x_0[/itex] doesn't matter a great deal but probably something like a/3 would be good.
It depends on the algorithm you choose and on the staring value (x0)Elsie93 said:http://www.infoocean.info/avatar2.jpg how long does that take to find the cube root of a 30-digit number, [on a 10-digit-display calculator] ?
(Just for future readers)scurty said:[itex]\frac{2ANS^3 -a }{3ANS^2}[/itex] and ... press the Enter key.
To find the cubic root of a number without using log keys, you can use the traditional method of repeated division. Divide the number by any number that you think might be close to the cubic root, then repeat the process with the result until you get a number that is very close to the cubic root. This method may take longer for larger numbers, but it is a reliable way to find the cubic root without using log keys.
Yes, there is a faster method called the "guess and check" method. It involves making an educated guess for the cubic root and then checking if the result is close enough to the actual cubic root. If it is not close enough, adjust your guess and repeat the process until you get a close enough result. This method is faster than repeated division, but it may require some trial and error.
Yes, most calculators have a function for finding the cubic root of a number. However, if you want to find the cubic root without using log keys, you may need to use the "guess and check" method or repeated division manually on the calculator.
You can use log keys to find the cubic root of a number, but it may not be the most efficient method. Also, some people may not have access to a calculator or device with log keys, so it is helpful to know alternate methods for finding the cubic root.
Yes, there are other methods such as the "prime factorization" method and the "decimal expansion" method. However, these methods may be more complex and require more mathematical knowledge. The "guess and check" and repeated division methods are the most commonly used for finding the cubic root without using log keys.