Quote:
Originally Posted by jinydu
That way, it would be possible to generalize the technique to cases where I don't know what x equals to beforehand.

For example, simplify the following:
cbrt(54+sqrt(2700))+cbrt(54sqrt(2700))
This time, I will not give out the answer a priori (although this particular case was also handpicked carefully). Also, the technique (maybe algorithm is an even better word) you use should also work for:
cbrt(10 + sqrt(108)) + cbrt(10  sqrt(108))