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
Root-mean-square deviation square root of the average of squared errors. The effect of each error on RMSD is proportional to the size of the squared error; thus larger errors have a disproportionately large effect on RMSD. Consequently, RMSD is sensitive to outliers. The RMSD of an estimator formula_1 with respect to an estimated parameter formula_2 is defined as the square root of the mean square error: For an unbiased estimator, the RMSD is the square root of the variance, known as the standard deviation. The RMSD of predicted values formula_4 for times "t" of a regression's dependent variable formula_5 with variables observed