Square root any nonnegative number, then the principal square root of −"x" is The right side (as well as its negative) is indeed a square root of −"x", since For every non-zero complex number "z" there exist precisely two numbers "w" such that : the principal square root of "z" (defined below), and its negative. There are two complex numbers that square to a given arbitrary non-zero imaginary number formula_11 with real formula_12 where the two-digit pattern {3, 6} repeats over and over again in the partial denominators. Since , the above is also identical to the following generalized continued fractions: The
Square root of 2 widely used constant. formula_81 The (approximate) aspect ratio of paper sizes under ISO 216 (A4, A0, etc.) is 1:. This ratio of lengths of the shorter over the longer side guarantees that cutting a sheet in half along a line parallel to its shorter side results in the smaller sheets having the same (approximate) ratio as the original sheet. Proof: Let formula_82 shorter length and formula_83 longer length of the sides of a sheet of paper, with Let formula_85 be the analogue ratio of the halved sheet, then Square root of 2 The square root of 2, or the (1/2)th