Square root of 3 billion digits. The fraction (…) for the square root of three can be used as an approximation. Despite having a denominator of only 56, it differs from the correct value by less than (approximately ). The rounded value of 1.732 is correct to within 0.01% of the actual value. Archimedes reported , accurate to (six decimal places) and (four decimal places), respectively. It can be expressed as the continued fraction , expanded on the right. It can also be expressed by generalized continued fractions such as which is evaluated at every second term. The following nested square expressions converge to
Square root of a matrix linear map is completely positive if and only if it is of the form where "k" ≤ "nm". Let {"E"} ⊂ C be the "n" elementary matrix units. The positive matrix is called the "Choi matrix" of Φ. The Kraus operators correspond to the, not necessarily square, square roots of "M": For any square root "B" of "M", one can obtain a family of Kraus operators "V" by undoing the Vec operation to each column "b" of "B". Thus all sets of Kraus operators are related by partial isometries. In quantum physics, a density matrix for an "n"-level quantum system