michael.eichberg@dhbw-mannheim.de, Raum 149B
1.0
TODO
Berechnung der Kubikwurzeln mit Hilfe eines einfachen Algorithmus.
Newton-Raphson algorithm,
How do you estimate cube roots to the nearest integer without a calculator? To find the cube root of N:
Express N as a product of a, a and b where a is any convenient number.
Take the average of a, a and b. This will be closer to the actual root than the initial estimate a.
Revise a and repeat the above steps till you get succeeding value close to the previous value.
You can ignore the higher decimals since the arithmetic average of the factors is equal to or greater than the actual root.
Example: to find the cube root of 5719:
Let us start with a factor,say 20.
Express 5719 as product of three factors of which two factors are 20 each.
5719=20*20*14.29
Average of the factors = 54.29/3=18
Express 5719 as product of three factors of which two factors are 18 each.
5719=18*317=18*18*17.6
Average of the factors = 53.6/3=17.86
This average is close to the initial estimate of 18. Further factorisation is not required.
So, the cube root of 5719 is about 17.86 or 18 after rounding off to the nearest integer.