The square root function

Definition

The square root function, denoted by f(x) = sqrt(x), is defined only for x ≥ 0 (domain: [0; +∞[). By definition, sqrt(x) is the positive number whose square is x.

Variations

The square root function is increasing over its entire domain [0; +∞[.

x	0	1	4	9	16
sqrt(x)	0	1	2	3	4

Graph

The graph of f(x) = sqrt(x) starts at the origin (0, 0) and rises more and more gradually: it resembles a half-parabola lying on its side. It does not exist for x < 0 and never descends.

Example

sqrt(25) = 5 because 5² = 25. sqrt(2) is an irrational number, approximately 1.414.

Common pitfall

sqrt(x²) is not always equal to x: sqrt(x²) = |x| (the absolute value of x). For example, sqrt((-3)^2) = sqrt(9) = 3, not -3. Similarly, sqrt(x) is never negative, even when x is a very large number.