How to evaluate $(8.024)^{1/3}$ from $(1+3x)^{1/3}$.I already expand it until $x^3$ but i still can't get the answer. I tried googling for the working using binomial theorem but i failed.
2026-04-02 11:22:29.1775128949
Evaluating a cube root
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Using Daniel's comment: $(8.024)^{1/3} = 2*(1+3\cdot0.001)^{1/3}$
so $x=0.001$
Taylor sequence: $(1+3x)^{1/3} = 1+x-x^2+\frac{5}{3}x^3$
Substituting $x=0.001$:
$(8.024)^{1/3} = 2*(1+3\cdot0.001)^{1/3} = 2(1+0.001-10^{-6}+\frac{5}{3}10^{-9}) = 2(1.0009990017) = 2.001998$