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The square root of 2 (approximately 1.4142) is the positive real number that, ... Square root of 2 is irrational, a collection of proofs; Haran, Brady (27 Jan 2012).
The square root of 2 was likely the first number proved irrational. [27] The golden ratio is another famous quadratic irrational number. The square roots of all natural numbers that are not perfect squares are irrational and a proof may be found in quadratic irrationals.
Hippasus is sometimes credited with the discovery of the existence of irrational numbers, following which he was drowned at sea. Pythagoreans preached that all numbers could be expressed as the ratio of integers, and the discovery of irrational numbers is said to have shocked them. However, the evidence linking the discovery to Hippasus is unclear.
Twelfth root of 2 [12] 1.05946 30943 59295 26456 [OEIS 10] Real root of = ... is irrational. If true, this will prove the twin prime conjecture. ...
Quadratic irrational numbers, irrational solutions of a quadratic polynomial ax 2 + bx + c with integer coefficients a, b, and c, are algebraic numbers. If the quadratic polynomial is monic (a = 1), the roots are further qualified as quadratic integers. Gaussian integers, complex numbers a + bi for which both a and b are integers, are also ...
The square root of 2 was the first such number to be proved irrational. Theodorus of Cyrene proved the irrationality of the square roots of non-square natural numbers up to 17, but stopped there, probably because the algebra he used could not be applied to the square root of numbers greater than 17. Euclid's Elements Book 10 is dedicated to ...
Enjoy a classic game of Hearts and watch out for the Queen of Spades!
For a while, the Pythagoreans treated as an official secret the discovery that the square root of two is irrational, and, according to legend, Hippasus was murdered for divulging it. [6] [7] [8] The square root of two is occasionally called "Pythagoras' number" or "Pythagoras' Constant", for example Conway & Guy (1996). [9]