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Square root of 2
Unique positive real number which when multiplied by itself gives 2 / From Wikipedia, the free encyclopedia
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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 or
. 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.
![]() The square root of 2 is equal to the length of the hypotenuse of an isosceles right triangle with legs of length 1. | |
Representations | |
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Decimal | 1.4142135623730950488... |
Continued fraction |
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