The combine/radical function is used to combine products of radicals of the same power that appear in an expression.

The main transformation made by combine/radical is

where  and  are both positive, (i.e.  ) and  where  are integers.

For example:  

If the condition  above is not satisfied, then let  where . Then expand   as   so that the condition is now satisfied.  If  is an integer, Maple applies this transformation automatically.  

For example: .

Suppose the sign of  is known to be negative, i.e. . Then expand  as   so that the positive part  can now be combined.  

For example:  

The new radical  needs to be simplified. The new radicand  is simplified by applying normal(x^m*y^n, expanded). For example: which after simplification yields

If the sign of  and  is not known, then combine will not combine the radicals because that is not correct for all  and  in general. For example  for negative  and .  The user has two possibilities to force Maple to combine radicals of unknown sign. The first is to use assume to tell Maple the sign of the radicands. The second is to specify the optional argument symbolic which will assume all radicands of unknown sign are real and positive.

If the sign of one radicand is unknown -- for example, suppose that  and  is unknown -- then combine will still combine the radicands  and  because  is known to be positive.