The square root of 5 is the positive real number that, when multiplied by itself, gives the prime 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 surd form as:
List of numbers Irrational and suspected irrational numbers γ ζ(3) √2 √3 √5 φ ρ δS e π δ Binary 10.0011110001101110… Decimal 2.23606797749978969… Hexadecimal 2.3C6EF372FE94F82C… Continued fraction 2 + 1 4 + 1 4 + 1 4 + 1 4 + ⋱ 2 + \cfrac{1}{4 + \cfrac{1}{4 + \cfrac{1}{4 + \cfrac{1}{4 + \ddots}}}} 5 . \sqrt{5}. \, It is an irrational algebraic number.[1] The first sixty significant digits of its decimal expansion are:
2.23606797749978969640917366873127623544061835961152572427089… (sequence A002163 in the OEIS). which can be rounded down to 2.236 to within 99.99% accuracy. The approximation 161 / 72 (≈ 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 1 / 10,000 (approx. 4.3×10−5). As of December 2013, its numerical value in decimal has been computed to at least ten billion digits.[2]