SOLUTION: detailed working for square root of 586576 using prime numbers

              586576
                /\
               2 293288
                   /\
                  2 146644
                     /\
                    2 73322
                       /\
                      2 36661
                         /\
                       61 601



For square root, the understood index is 2:



Divide the index 2 into the exponent of 2, which is 4, getting 2,
then putting 22 out in front.





Erase the index when it is 2:





Edwin