[Python] Nth root of y

Question

so im trying to write a code to learn with that will return what times itself x times = y or the nth root of y.
i know its a logic error because it runs but i doesnt do what i want i think the error is in the last print statement or in how im manipulating the variables to try the next case i have a feeling this method is floored but im not sure how my next attempt will be to use % test case instead of percentage of the answer i want

https://code.sololearn.com/cPHAZNLLpsZ0/#py

Answer 1

First of all, powers in python are done with the ** operator instead of ^. This also means you can find nth roots like this: x ** (1/n)

But doing it "by hand" is an interesting challenge. For square roots there is the well known babylonian method: Lets say we want to find √100. First we take a guess `x`, say 5, doesn't really matter. Then you do:

(100/x + x) / 2

and that is your new x. You take the midway point between your guess and the reciprocal so to say.

For higher roots there is Newton's method:

Say we want to find x = ³√100.

then x³ - 100 = 0 with a bit of algebra, which is a polynomial where we want to find the root. The derivative of x³ - 100 is 2x².

Newtons method therefor says:

Take a guess x, say 5, doesn't matter. Do

x - (x³ - 100) / (2x²)

And that is your new x. Do that a couple of times and you get a pretty good estimate for ³√100.

I hope that wasn't too maths-heavy.

Answer 2

Schindlabua that makes me feel like I need to take a refresher in mathematics. Lol
Maybe I'm just getting old, been close to 30 yrs since my last math class. Lol

Answer 3

Nth root example from;

https://www.google.com/amp/s/www.geeksforgeeks.org/n-th-root-number/amp/

HTH

https://code.sololearn.com/cyd8FnKTVtkn/?ref=app

Answer 4

ChaoticDawg Honestly I just know it's a thing and I look up the details as needed :P My uni maths was like 5 years ago though so it's a bit fresher, ha.