Square root of 5

Square root of 5

Rationality	Irrational
Representations
Decimal	2.23606797749978969...
Algebraic form	${\displaystyle {\sqrt {5}}}$
Continued fraction	${\displaystyle 2+{\cfrac {1}{4+{\cfrac {1}{4+{\cfrac {1}{4+{\cfrac {1}{4+\ddots }}}}}}}}}$

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:

${\displaystyle {\sqrt {5}}.\,}$

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 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.^[2]