Search results
Results From The WOW.Com Content Network
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 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.
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 ...
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
Since taking the square root is the same as raising to the power 1 / 2 , the following is also an algebraic expression: 1 − x 2 1 + x 2 {\displaystyle {\sqrt {\frac {1-x^{2}}{1+x^{2}}}}} An algebraic equation is an equation involving polynomials , for which algebraic expressions may be solutions .
For example, the square root of 2 is an irrational number, but it is not a transcendental number as it is a root of the polynomial equation x 2 − 2 = 0. The golden ratio (denoted φ {\displaystyle \varphi } or ϕ {\displaystyle \phi } ) is another irrational number that is not transcendental, as it is a root of the polynomial equation x 2 − ...
The square root of 2 is equal to the length of the hypotenuse of a right triangle with legs of length 1 and is therefore a constructible number. In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length | | can be constructed with compass and straightedge in a finite number of steps.
A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred by using ordinal numbers, as in fourth root, twentieth root, etc. The computation of an n th root is a root extraction. For example, 3 is a square root of 9, since 3 2 = 9, and −3 is also a square root of 9, since (−3) 2 = 9.