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. 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. The graph of f(x)xa+b can be obtained by translating the graph of f(x)x to a units to the right and then b units up. 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.