31. Cubic root calculation without the iteration formula
1 ( x )
Formula: Yn + 1 = Yn + --- ( --- - Yn )
3 ( y )
As with the 0uadrat root, it is necessary to have a first Initial
approximation is estimated. For this purpose, the Radicandin front of the
comma from left to the left in groups of three digits ...
The number of groups again gives you the number of digits before the
Decimal point.
Again, it should be noted that the extreme left group only one
or two digits can exist, but still be evaluated as a group.
3_________ 2 Triplets and therefore
Example :
√
2 847,39 2 Ask before the Decimal point
3_________
Example :
√
279,489
Here is a group of three, so that the number of digits before the decimal
point is 1 digit.
The cube root of 279 is about 6.5.
Now you can start with the calculation according to the iteration
formula.
1 (279‚43 )
6.5 + --- (------ - 6.5)
= 6 538 304 1st Approximation
3 ( 6,5 2 )
1 ( 279,48 )
6,538 304 + --- (--------- - 6,538 3042 ) = 6,538 080 2nd Approximation
3 (6,538 080 2 )
Sample: 6.538 080 3 = 279.48
======
Walk through
Sequence of the calculation
Function key
Display
---------------------------------------------------------------------
1. Clear the memory
*I, *II
2. Decimal point position
6
3. Enter
279,45
+II
979,400 000
4. Enter
6,5
+I
6,500 000
5.
X
6,500 000
6.
Xn
42,250 000
7.
+
42,250 000
8. Recall
II
279,480 000
33
