Guess and find the Cube Root!!
Let the no., whose cube root is to be calculated, be "a"
For example, let a=6
Begin with a guess, say x, to be its cube root.
In this case x=3/2
*** This guess is based on simple reasoning that cube of 2 is 8 and therefore 2 is too high and cube of 1 is 1 which means 1 is very low.The better the guess, the accurate the result ***
Now, we have a formula-
Y = 1/3[2x + a/(x*x)]Y = 1/3[2*3/2 + 6/(9/4)] = 1/3[3 + 24/9] = 51/27 = 1.888888
Repeat the process by taking x = 51/27
The process can be repeated successively to get more accurate result, by taking Y=x.
Example2 : to find cube root of a=89
let x=9/2 then
Y = 1/3[2*9/2 + 89/(81/4)]
= 1/3[9 + 4.3950]
= 3 + 1.4650
= 4.4650
Repeat the process by taking x = 4.4650
N!$H@NT