Calculations are normally performed numerically wherever possible.
For example, the calc-sqrt command, or sqrt function in an
algebraic expression, produces a numeric answer if the argument is a
number or a symbolic expression if the argument is an expression:
2 Q pushes 1.4142 but ' x+1 RET Q pushes `sqrt(x+1)'.
In symbolic mode, controlled by the m s (calc-symbolic-mode)
command, functions which would produce inexact, irrational results are
left in symbolic form. Thus 16 Q pushes 4, but 2 Q pushes
`sqrt(2)'.
The shift-N (calc-eval-num) command evaluates numerically
the expression at the top of the stack, by temporarily disabling
calc-symbolic-mode and executing = (calc-evaluate).
Given a numeric prefix argument, it also
sets the floating-point precision to the specified value for the duration
of the command.
To evaluate a formula numerically without expanding the variables it
contains, you can use the key sequence m s a v m s (this uses
calc-alg-evaluate, which resimplifies but doesn't evaluate
variables.)