Real Number Whole Numbers:0,1,2,3,4,5,6,7,8,9,10,etc. Counting Numbers:1,2,3,4,5,6,7,8,etc. Natural Numbers:which is whole or counting numbers depends on the topic Integers:-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10,etc.
It can work reasonably well to start with the largest square less than the target number, repeating that approach for the remaining differences. When more squares than necessary are asked for, then the first square chosen may need to be the square of a number 1 less than the largest possible.
The approach where a cube is required can work the same way.
