Math Help - Calculation with Big Oh or Theta

I'm dealing with calculation in terms of Big Oh or Theta notations.

For example,

If I want to simplify O(n^k * sqrt ( a* n^m - n^p )) as much as possible, where a is positive constant and k,m,p are positive unknown, then is it possible for me to remove the term n^p?

Then, the final answer is O(n^k * sqrt (n^m)). Is this correct?

If I want to simplify O(n^k * sqrt ( a* n^m - n^p )) as much as possible, where a is positive constant and k,m,p are positive unknown

Is there a difference between a constant and an unknown in this context?

Then, the final answer is O(n^k * sqrt (n^m)). Is this correct?

Yes. I would write it as n^{k + m/2}.

Thanks for your reply.

I think there is difference. If a is not constant, i.e., function of n, then a cannot be just cancelled... Anyway, I think a is not really important in my original problem.