In a sense these square roots are the very simplest irrational numbers, because they can be represented with a simple repeating pattern of integers. That is, a certain pattern of partial denominators repeats indefinitely in the continued fraction. Lagrange found that the representation of the square root of any non-square positive integer as a continued fraction is periodic. One of the most intriguing results from the study of irrational numbers as continued fractions was obtained by Joseph Louis Lagrange c. In geometrical terms, the square root function maps the area of a square to its side length. The square roots of small integers are used in both the SHA-1 and SHA-2 hash function designs to provide nothing up my sleeve numbers. (usually just referred to as the 'square root function') is a function that maps the set of nonnegative real numbers onto itself. In all other cases, the square roots of positive integers are irrational numbers, and therefore have non-repeating digits in any standard positional notation system. In mathematics, a square root of a number x is a number y such that y 2 = x in other words, a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x.
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