| Command Summary | Command Syntax | Calculator Compatibility | Token Size |
|---|---|---|---|
| Takes the square root of a number. | √(number) | This command works on all calculators. | 1 byte |
Menu Location
N/A
The √() Command
The √() command takes the square root of a value: √(x) is a number that, when multiplied by itself, gives x. It's a special case of the ^ and 68k:root() commands: √(x) = x^(1/2) = root(x,2).
Unless the calculator is in approximate mode, or you force it to approximate (by pressing ♦+ENTER, or using 68k:approx()), it won't try to evaluate all square roots: it will take the square root of perfect squares, otherwise, it will just take out all the square factors (for instance, √(20) is simplified to 2√(5)).
For positive numbers, √() will return the positive square root; more generally, if the result is complex (and if the calculator is in complex number mode), the result of √() will be the one with non-negative real part.
:√(16)
4
:√(-12)
2*√(3)*i
If the square root of a list is taken, it will take the square root of every element of the list.
Advanced Uses
The √() of a matrix is not (in general) the same as taking the square root of every element of the matrix. A different definition is used to compute the result; see 68k:matrices. It requires the matrix to be square and diagonalizable in order to apply.
Error Conditions
230 - Dimension happens when taking the square root of a non-square matrix.
665 - Matrix not diagonalizable happens when diagonalization (used to take square roots of matrices) fails.
800 - Non-real result happens when taking the square root of a negative or complex number, in real number mode.