Article 11 — Appendix A.29

√ or sqrt — square root function

Category. Mathematics.

Abstract. Square root: definition, graph, properties and identities.

References. This article is a part of scientific calculator Li-L, scientific calculator Li-X, scientific calculator Li-Lc and scientific calculator Li-Xc products.

1. Definition

Square root function is inverse of the power function with power a = 2

The square root is denoted with radical symbol:

Square root is equivalent to the power of one second:

2. Graph

Square root function defined for non-negative part of real axis — so, its domain is [0, +∞). Function graph is depicted below — fig. 1.

Function codomain non-negative part of the real axis: [0, +∞).

3. Identities

Take into account, that because of square root defined only for non-negative values, and power of two defined everywhere, the order of these two functions makes difference:

and as well

Reciprocal argument:

Product and ratio of arguments:

Power of argument:

4. Solution of quadratic equation

Quadratic equation

has roots

For equation with even coefficient for the first power ax² + 2bx + c = 0

roots have simplified form

5. Solution of normalized quadratic equation

Normalized quadratic equation x² + bx + c = 0

has roots

And equation with even coefficient for the first power x² + 2bx + c = 0

has the simplest form for its roots

6. Support

Square root function √ or sqrt is supported in:

• Scientific calculator Li-L
• Scientific calculator Li-X — advanced

Square root function of the complex argument √ or sqrt is supported in:

• Scientific calculator Li-Lc — complex numbers
• Scientific calculator Li-Xc — complex numbers, advanced

7. How to use

To calculate square root of the number:

sqrt(2);

or

√(2);

To calculate square root of the current result:

sqrt(Rslt);

or

√(Rslt);

To calculate square root of the number x in memory:

sqrt(Mem[x]);

or

√(Mem[x]);