Square root of 3
| Binary | 1.10111011011001111010… |
| Decimal | 1.7320508075688772935… |
| Hexadecimal | 1.BB67AE8584CAA73B… |
| Continued fraction | |
The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3. It is more precisely called the principal square root of 3, to distinguish it from the negative number with the same property. It is denoted by
The square root of 3 is an irrational number. It is also known as Theodorus' constant, named after Theodorus of Cyrene, who proved its irrationality.
The first sixty digits of its decimal expansion are:
As of December 2013, its numerical value in decimal has been computed to at least ten billion digits.
The fraction 97/56 (1.732142857…) for the square root of three can be used as an approximation. Despite having a denominator of only 56, it differs from the correct value by less than 1/10,000 (approximately 9.2×10−5). The rounded value of 1.732 is correct to within 0.01% of the actual value.
Archimedes reported (1351/780)2
> 3 > (265/153)2
, accurate to 1/608400 (six decimal places) and 2/23409 (four decimal places), respectively.
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