SQUARE ROOT OF 2
How was the square root of 2 often represented geometrically?
Geometrically the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem.
What is an approximation of its numerical value?
Its numerical value, truncated to 65 decimal places, is: 1.41421356237309504880168872420969807856967187537694807317667973799
What are some approximations used for the square root of two?
The approximation 99/70 (≈ 1.41429) for the square root of two is frequently used. Despite having a denominator of only 70, it differs from the correct value by less than 1/10,000 (approx. 7.2 × 10−5). The approximation 665857/470832 is valid to within 1.13 x 10−12: its square is 2.0000000000045....
What is the record for the closest approximation of the square root of two?
The record is currently 2 trillion digits, held by Alexander Yee since February 9, 2012. Among mathematical constants with computationally challenging decimal expansions, only π has been calculated more precisely.
What is the square root of 2?
The square root of 2, written in mathematics as √2 or 2½ is the positive algebraic number that, when multiplied by itself, gives the number 2. Technically, it is called the principal square root of 2, to distinguish it from the negative number with the same property.
