Properties
The principal square root function (usually just referred to as the "square root function") is a function that maps the set of non-negative real numbers onto itself. In geometrical terms, the square root function maps the area of a square to its side length.
The square root of x is rational if and only if x is a rational number that can be represented as a ratio of two perfect squares. (See square root of 2 for proofs that this is an irrational number, and quadratic irrational for a proof for all non-square natural numbers.) The square root function maps rational numbers into algebraic numbers (a superset of the rational numbers).
For all real numbers x
(see absolute value)
For all non-negative real numbers x and y,
and
The square root function is continuous for all non-negative x and differentiable for all positive x. If f denotes the square-root function, its derivative is given by:
The Taylor series of √1 + x about x = 0 converges for |x| ≤ 1 and is given by
which is a special case of a binomial series.
Read more about this topic: Square Root
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