Unique positive real number which when multiplied by itself gives 2
"Pythagoras's constant" redirects here. Not to be confused with Pythagoras number.
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 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.
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]
The squarerootof2 (approximately 1.4142) is a positive real number that, when multiplied by itself or squared, equals the number 2. It may be written...
mathematics, a squarerootof a number x is a number y such that y 2 = x {\displaystyle y^{2}=x} ; in other words, a number y whose square (the result of multiplying...
Methods of computing square roots are algorithms for approximating the non-negative squareroot S {\displaystyle {\sqrt {S}}} of a positive real number...
{\textstyle {\sqrt {3}}} or 3 1 / 2 {\displaystyle 3^{1/2}} . It is more precisely called the principal squarerootof 3 to distinguish it from the negative...
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In mathematics, the root mean square (abbrev. RMS, RMS or rms) of a set of numbers is the squarerootof the set's mean square. Given a set x i {\displaystyle...
mathematics, the squarerootof a matrix extends the notion ofsquareroot from numbers to matrices. A matrix B is said to be a squarerootof A if the matrix...
The squarerootof 7 is the positive real number that, when multiplied by itself, gives the prime number 7. It is more precisely called the principal square...
representation of an approximation of2 127 {\textstyle {\sqrt {2^{127}}}} . This results in the first approximation of the inverse squarerootof the input...
A squarerootof a 2×2 matrix M is another 2×2 matrix R such that M = R2, where R2 stands for the matrix product of R with itself. In general, there can...
length of a side of the square. This value, known as the squarerootof2 or Pythagoras' constant, was the first number proven to be irrational. A square can...
early mathematical results, including an approximation of the squarerootof2 and the statement of the Pythagorean theorem. Baudhayana's Śrauta sūtras related...
The root mean square deviation (RMSD) or root mean square error (RMSE) is either one of two closely related and frequently used measures of the differences...
-man(x) | mortal(x). man(socrates). -mortal(socrates). end_of_list. A proof that the squarerootof2 is irrational can be expressed this way: formulas(assumptions)...
{\displaystyle \left({\tfrac {1}{2}}\right)} , real numbers such as the squarerootof2 ( 2 ) {\displaystyle \left({\sqrt {2}}\right)} and π, and complex...
symbol, radical sign, root symbol, radix, or surd is a symbol for the squareroot or higher-order rootof a number. The squarerootof a number x is written...
mathematics, a functional squareroot (sometimes called a half iterate) is a squarerootof a function with respect to the operation of function composition...
every real number other than zero (which has one double squareroot). In contexts in which use of the letter i is ambiguous or problematic, the letter j...
rootof degree 2 is called a squareroot (usually written without the n as just x {\displaystyle {\sqrt {x}}} ) and a rootof degree 3, a cube root (written...
sexagesimal approximation to the squarerootof2, the length of the diagonal of a unit square. This number is given to the equivalent of six decimal digits, "the...
Retrieved 2 October 2022. Alfeld, Peter (16 August 1996). "Why is the squarerootof2 irrational?". Understanding Mathematics, a study guide. Department of Mathematics...
irrationals to quadruples of integers, so their cardinality is at most countable; since on the other hand every squarerootof a prime number is a distinct...
sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the squarerootof2. This sequence...
construction or as a formula of a formal language. For example, the positive squarerootof2, 2 {\displaystyle {\sqrt {2}}} , can be defined as the unique...
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