The Art of Interface
+49 89 8999640

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

x2

The square root is denoted with radical symbol:

x

Square root is equivalent to the power of one second:

xx1/2

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.

Fig. 1. Graph of the square root function y = sqrt x Fig. 1. Graph of the square root function y = √x.

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:

x2x
√(x2) ≡ |x|

and as well

x ≡ signx √(x2)

Reciprocal argument:

√(1/x) = 1 /√x

Product and ratio of arguments:

√(xy) = √|x|√|y|
√(x/y) = √|x| /√|y|

Power of argument:

√(xa) = √|x|a ≡ |x|a/2

4. Solution of quadratic equation

Quadratic equation

ax2 + bx + c = 0

has roots

x = [−b ± √(b2 − 4ac)] /(2a)

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

roots have simplified form

x = [−b ± √(b2ac)] /a

5. Solution of normalized quadratic equation

Normalized quadratic equation x2 + bx + c = 0

has roots

x = [−b ± √(b2 − 4c)] /2

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

has the simplest form for its roots

x = −b ± √(b2c)

6. Support

Square root function or sqrt is supported in:

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

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]);