is there any method to find cube root of a real number without using logarithm table? I mean a simple method.?

Question

i want to find the cuberoot of a real number without using any calculator or computer or log.

Answer 1

No. Calculators have internal algorithms built by means of which they determine square root. They have to have a number of cube roots programmed in because there is no such algorithm (that we know of) for cube roots. The best I can do is give a close approximation for some cube roots.

for the cube root of 127, you take the cube root of 125, which is five, and add a derivative times a difference. The premise is that (dy/dx)*dx is approximately dy.

if y = x^(1/3), then dy/dx = (1/3)*x^(-2/3)

and, if x = 5, this is the same as 1/(3*25) = 1/75

multiply this by the difference between 125 and 127, and you get that the cube root of 127 is approximately the cube root of 125 plus 2/75. This is a pretty good approximation, but only because 127 is really close to 125. This method would be terrible for the cube root of 59, for example.

The method is probably called approximation by differentials. I have forgotten.

This was probably not as simple as you wanted, but it really can't be that simple.

Answer 2

Left alone, on a desert island, without any means than a pencil and a sheet of paper, I would proceed as such:

Iteratively! That is by trial and error

OK, imagine that you have to calculate the cube root of 25

2x2x2=8
3x3x3=27

so it is between 2 and 3, probably rather towards 3

I try 2.9

2.9x2.9x2.9=29x29x29 x 1/1000

= 24389/1000 =24,389

So it is between 2.9 and 3.0, rather towards 2.9
So I try with 2.94

and so on

It works!

Answer 3

You can play a high-low game. For instance, find the cubed root of two. 1^3=1 and 2^3=8 so since 2 is between 1 and 8, the cubed root of two is between 1 and 2. Then on to decimals, 1.1^3=1.331, 1.2^3=1.728, 1.3^3=2.197 so cubed root of two is between 1.2 and 1.3.

An iterative approach (which has a basis in calculus but the actual steps are not calculus based) is called Newton's Method. To find the cubed root of 'a' you would start with a good guess which you call x0 then you apply the formula x(n+1)=(2*xn^3+a)/(3*xn^2). For the cubed root of two, start with x0=1, then x1=4/3 then x2=(2*(4/3)^3+2)/(3*(4/3)^2)=91/72. Which is darn close, then x3=(2*x2^3+2)/(3*x2^2) would be 1126819/894348 etc.....

Answer 4

there is a way ... I think it involves series ... figure that there is a way to get the root or power of anything, at least approximately because calculators do it in milliseconds.

There are all kinds of tricks and approximations in computer science used to approximate roots power and trigonometric
and such.

BUT ... I cannot tell you how specifically! ;-)

Answer 5

There is lots of computer programs to calculate this kind of matters

Answer 6

Raj, I admire your mathematical expertise.
I can't answer your question (and I know it means I probably deserve a thumbs down), but I just wanted to say I hope someone answers your question the way you answer everyone else's.

Answer 7

There is not. In fact there is not even a way to do it with square roots.

Answer 8

it can be resolved by using factorization method,i.e.,
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but it not find the cube root of all the numbers.

Answer 9

(substitution).trial and error,too low too high,narrow it down

Answer 10

as above