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

The square root of 2 (approximately 1.4142) is a positive real number that, when multiplied by itself or squared, equals the number 2. It may be written in mathematics as ${\sqrt {2}}$ or $2^{1/2}$ . 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.^[1] 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:^[2]

1.41421356237309504880168872420969807856967187537694807317667973799

^ Fowler, David H. (2001), "The story of the discovery of incommensurability, revisited", Neusis (10): 45–61, MR 1891736
^ "A002193 - OEIS". oeis.org. Retrieved 2020-08-10.

[1] Fowler, David H. (2001), "The story of the discovery of incommensurability, revisited", Neusis (10): 45–61, MR 1891736

[2] "A002193 - OEIS". oeis.org. Retrieved 2020-08-10.

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