The √() Command


Command Summary

Takes the square root of a number.

Command Syntax


Menu Location

This command can't be found in any menu besides the command catalog.

Calculator Compatibility

This command works on all calculators.

Token Size

1 byte

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 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 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.


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 Matrices and Their Commands. 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.

Related Commands

Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-Noncommercial-No Derivative Works 2.5 License.