My method is certainly not as sophisticated as others here but since it was different from these others, I will post it as well. The solution should obviously

My method is certainly not as sophisticated as others here but since it was different from these others, I will post it as well. The solution should obviously be somewhere between 20 and 30. Since I knew 25^2 = 625 already, I multiplied by 25 to arrive at 25^3 = 15625. From there I used the approximation (1 + x)^n = 1 + nx which works if x << 1. 19683 = 15625*(1 + x) = 25^3*(1 + x) with x ~= 4000/15625 ~= 0.25. This stretches the condition ("x << 1") for the approximation a lot but so be it. (1 + 1/4)^1/3 ~= 1 + 1/12. 25*(1 + 1/12) ~= 27 Good enough ;)