Solve without using a calculator (0.9484)^1/3?

(1+x)^n = 1 + nx + n(n-1)(x^2)/2! + ....

and can accepted as

(1+x)^n = 1 + nx

we have
n=1/3
and
1+x=0.9484 --->> x= - 0.0516

so
(1+x)^n = 1 + nx
(1-0.0516)^(1/3) =1+(1/3)(-0.0516)

(1+x)^(1/3)=1-(1/3)*(0.0516)
=1-0.0172 = 0.9828

if you use a calculator (0.9484)^1/3=0.982495376

so the answer is 99.97 % accurate.

0.9484= 1- 0.0516, so

(0.9484)^1/3 = (1- 0.0516)^(1/3).....which can be expanded using the binomial theorum.

Use the trial and test method, notice that 21^3=9261 then keep approximate until you get a close number. It will take a bit of a time to figure out.