Square root of 2

Square root of 2

The square root of 2 is equal to the length of the hypotenuse of an isosceles right triangle with legs of length 1.
Representations
Decimal	1.4142135623730950488...
Continued fraction	${\displaystyle 1+{\cfrac {1}{2+{\cfrac {1}{2+{\cfrac {1}{2+{\cfrac {1}{2+\ddots }}}}}}}}}$

The square root of 2 (approximately 1.4142) is the positive real number that, when multiplied by itself or squared, equals the number 2. It may be written as ${\displaystyle {\sqrt {2}}}$ or ${\displaystyle 2^{1/2}}$. It is an algebraic number, and therefore not a transcendental 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 60 decimal places:

1.414213562373095048801688724209698078569671875376948073176679