Mathematical constants | Quadratic irrational numbers
Square root of 3
The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3. It is denoted mathematically as or . It is more precisely called the principal square root of 3 to distinguish it from the negative number with the same property. The square root of 3 is an irrational number. It is also known as Theodorus' constant, after Theodorus of Cyrene, who proved its irrationality. As of December 2013, its numerical value in decimal notation had been computed to at least ten billion digits. Its decimal expansion, written here to 65 decimal places, is given by OEIS: : 1.732050807568877293527446341505872366942805253810380628055806 The fraction (1.732142857...) can be used as a good approximation. Despite having a denominator of only 56, it differs from the correct value by less than (approximately , with a relative error of ). The rounded value of 1.732 is correct to within 0.01% of the actual value. The fraction (1.73205080756...) is accurate to . Archimedes reported a range for its value: . The lower limit is an accurate approximation for to (six decimal places, relative error ) and the upper limit to (four decimal places, relative error ). (Wikipedia).
