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My little arithmetic discovery: finding tetrational square roots with the help of a chain root
Finding tetrational square roots with the help of a chain root:
For example, you need to find the square root of two:
1st. elevation of 2 to the power of 2 equals 4.
2nd. Find that the square root of 4 is 2.
The 3rd multiplication of 2 by 2 is 4.
4. Finding the Root of 4 Early 1.4142
5th multiplication of 1.4142 by 2 equals 2.8284
On the 6th, we find that the root of 2.8284 out of 4 is 1.6325
6th 1.6325 multiplied by 2 equals 3.265
After a large number of iterations, the resulting value drops to 1.5596...
1.559^1.559=2, which had to be proved.
Here is a screenshot of the calculation:
https://ibb.co/30yRn5H
Here is a screenshot of calculating tetrational square root of three
https://forumimage.ru/show/112089058
If you want to calculate the square tetrational root of four, five, six, etc., then just substitute it on the site
https://www.desmos.com/scientific?lang=ru in the scientific calculator 4^2, 5^2, 6^2, etc. n^2, but this is in theory, in practice the calculation with desmos.com is not gives high accuracy, but you need a more powerful calculator
Post scriptum: The convergence of the computation chain to an exact result is very slow and slows down as the number from which the tetrational square root is calculated increases