#### 6.4.5 Symbolic Mode

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.)