Mathematical constants | Quadratic irrational numbers
Square root of 7
The square root of 7 is the positive real number that, when multiplied by itself, gives the prime number 7. It is more precisely called the principal square root of 7, to distinguish it from the negative number with the same property. This number appears in various 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: 2.64575131106459059050161575363926042571025918308245018036833.... which can be rounded down to 2.646 to within about 99.99% accuracy (about 1 part in 10000); that is, it differs from the correct value by about 1/4,000. The approximation 127/48 (≈ 2.645833...) is better: despite having a denominator of only 48, it differs from the correct value by less than 1/12,000, or less than one part in 33,000. More than a million decimal digits of the square root of seven have been published. (Wikipedia).
