root 5.1.1

The square root of 2 (approximately 1.4142) is a positive real number that, when multiplied by itself, equals the number 2. It may be written in mathematics as





2




{\displaystyle {\sqrt {2}}}
or




2

1

/

2




{\displaystyle 2^{1/2}}
, and is an algebraic number. Technically, it should be called the principal square root of 2, to distinguish it from the negative number with the same property.
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. It was probably the first number known to be irrational. The fraction 99/70 (≈ 1.4142857) is sometimes used as a good rational approximation with a reasonably small denominator.
Sequence A002193 in the On-Line Encyclopedia of Integer Sequences consists of the digits in the decimal expansion of the square root of 2, here truncated to 65 decimal places:
1.41421356237309504880168872420969807856967187537694807317667973799

You do not have permission to view the full content of this post. Log in or register now.