Draft:Finding Tetrational square Roots Using a Chain Root

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