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β5
The square root of 5 is the positive real number that, when multiplied by itself, gives the prime number 5 (number), 5. It is more precisely called the principal square root of 5, to distinguish it from the negative number with the same property. This number appears in the fractional expression for the golden ratio. It can be denoted in nth root, surd form as \sqrt. It is an irrational number, irrational algebraic number. The first sixty significant digits of its decimal expansion are: : , which can be rounded down to 2.236 to within 99.99% accuracy. The approximation (β 2.23611) for the square root of five can be used. Despite having a denominator of only 72, it differs from the correct value by less than (approx. ). As of January 2022, the numerical value in decimal of the square root of 5 has been computed to at least 2,250,000,000,000 digits. Rational approximations The square root of 5 can be expressed as the simple continued fraction : [2; 4, 4, 4, 4, 4,\ldots] = 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Number
In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and in many other branches of mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives. The set of real numbers, sometimes called "the reals", is traditionally denoted by a bold , often using blackboard bold, . The adjective ''real'', used in the 17th century by RenΓ© Descartes, distinguishes real numbers from imaginary numbers such as the square roots of . The real numbers include the rational numbers, such as the integer and the fraction . The rest of the real numbers are called irrational numbers. Some irrational numbers (as well as all the rationals) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
