| dbo:abstract
|
- The square root of 6 is the positive real number that, when multiplied by itself, gives the natural number 6. It is more precisely called the principal square root of 6, to distinguish it from the negative number with the same property. This number appears in numerous geometric and number-theoretic contexts. It can be denoted in surd form as: and in exponent form as: It is an irrational algebraic number. The first sixty significant digits of its decimal expansion are: 2.44948974278317809819728407470589139196594748065667012843269.... which can be rounded up to 2.45 to within about 99.98% accuracy (about 1 part in 4800); that is, it differs from the correct value by about 1/2,000. It takes two more digits (2.4495) to reduce the error by about half. The approximation 218/89 (≈ 2.449438...) is nearly ten times better: despite having a denominator of only 89, it differs from the correct value by less than 1/20,000, or less than one part in 47,000. Since 6 is the product of 2 and 3, the square root of 6 is the geometric mean of 2 and 3, and is the product of the square root of 2 and the square root of 3, both of which are irrational algebraic numbers. NASA has published more than a million decimal digits of the square root of six. (en)
|
