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 (1.41421356...). The Rhind Mathematical Papyrus is a copy from 1650 BC of an earlier Berlin Papyrus and other textspossibly the Kahun Papyrusthat shows how the Egyptians extracted square roots by an inverse proportion method. In Ancient India, the knowledge of theoretical and applied aspects of square and square root was at least as old as the "Sulba Sutras", dated around 800–500 BC (possibly much earlier). A method for finding very good approximations to the square roots of 2 and 3 are given in the "Baudhayana Sulba Sutra". Aryabhata in the "Aryabhatiya" (section 2.4), has given a method for finding the