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#### 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.)