Finding the Nth Root of a Number

Ronald Finnerty
A couple of useful links'

https://www.exploringbinary.com/binary-converter/
https://indepth.dev/the-simple-math-behind-decimal-binary-conversion-algorithms

Unfortunately, neither how to get the square root of a binary number. Here are the basics:

(see Figure 1 below)

You can convert a whole number to binary using the DEC2BIN function or by an algorithm shown in Fig1. It also shows how to convert a decimal to binary. Some decimals can not be converted exactly, so we stop when you get a repeated pattern.

For the decimal algorithm, you can use the TEXTJOIN function to get the decimal part from the algorithm.

To get a square root you can use the Babylonian algorithm {fig2), I just used the SQRT function in K2 of 65 to get the integer binary. And used a version of the TEXTJOIN for the decimal part.

(see Figure 2 below)

Of course, you don't need the Babylonian algorithm for the fraction just get it from the decimal SQRT function.

I'm afraid there is serious confusion here:

- n^(1/5) gives the fifth root of n
- n^-(5 ) gives the inverse of n^5

By example, if n = 10,
n^2 = 100
n^-2 = 0.01
n^(1/2) = 3.16227766 (this is the square root of 10)

So, using fractional exponents or negatives exponents is COMPLETELY DIFFERENT !

this did not answer the finding nth root question. It merely shows how nth root calculation work.
If I have a number and need to find the nth root of base 2 of the number i am no further along with your solution.
i only know the answer is 2^1/n so how do i find n?

Just to be pedantic, I'll point out that Maarten is almost correct. He said:
2^-1 for instance is 0.5 (2/2^1)
2^-3 is 0.125 (2/2^3)
When he meant
2^-1 for instance is 0.5 (1 / 2^1)
2^-3 is 0.125 (1 / 2^3)

You can even use negative exponents.
2^-1 for instance is 0.5 (2/2^1)
2^-3 is 0.125 (2/2^3)
etc.
And so on.
Of course fractional negative exponents work also, but that is more complicated

The POWER function also works here,

POWER(B7,1/5)