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 Square root In mathematics, a square root of a number "a" is a number "y" such that ; in other words, a number "y" whose "square" (the result of multiplying the number by itself, or ) is "a". For example, 4 and −4 are square roots of 16 because . Every nonnegative real number "a" has a unique nonnegative square root, called the "principal square root", which is denoted by , where √ is called the "radical sign" or "radix". For example, the principal square root of 9 is 3, which is denoted by = 3, because and 3 is