Can anyone show me how you would work out, basically, $nth$ roots? Say you want to approximate the value of $\sqrt[n]{x+y}$, how would you use Newton's method using: $$x_{k+1}=x_k+\frac{f(x)}{f'(x)}$$ One approximation from this link gives an approximation of the $nth$ root: $$\sqrt[n]{x^n+y}=x+\frac{y}{nx^{n-1}}$$ However, the approximation is not exactly very exact especially with small numbers. Hope anyone can usher me in.
2026-02-22 19:50:51.1771789851
How to approximate $\sqrt[n]{x+y}$ using Newton's method
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