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 nonnegative. The term (or number) whose square root is being considered is known as the "radicand". The radicand is the number or expression underneath the radical sign, in this example 9. Every positive number "a" has two square roots: , which is positive, and −, which is negative. Together, these two roots are denoted as ± (see ± shorthand). Although the principal square root of a positive number is only one of its two square roots, the designation ""the" square root" is often used to refer to the "principal square root". For positive "a", the principal square root can also