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Number whose square is a given number
In mathematics, a square root of a number x is a number y such that y2=x; in other words, a number y whose square (the result of multiplying the number
Square_root
Unique positive real number which when multiplied by itself gives 2
The square root of 2 (approximately 1.4142) is the positive real number that, when multiplied by itself or squared, equals the number 2. It may be written
Square_root_of_2
Algorithms for calculating square roots
Square root algorithms compute the non-negative square root S of a positive real number S. Since all square roots of natural numbers, other than of perfect
Square_root_algorithms
Square root of the mean square
In mathematics, the root mean square (abbrev. RMS, rms or rms) of a set of values is the square root of the set's mean square. Given a set x i {\displaystyle
Root_mean_square
Root-finding algorithm
Fast inverse square root, sometimes referred to as Fast InvSqrt() or by the hexadecimal constant 0x5F3759DF, is an algorithm that estimates 1 / x {\textstyle
Fast_inverse_square_root
Principal square root of minus 1
additive inverses of each other, while zero has only zero as its (double) square root. Historically, the imaginary unit was denoted by −1, though this is
Imaginary_unit
Irrational algebraic number
In mathematics, the square root of 10 is the positive real number that, when multiplied by itself, gives the number 10. It is approximately equal to 3
Square_root_of_10
Mathematical symbol denoting a root
radical symbol, radical sign, root symbol, or surd is a symbol for the square root or higher-order root of a number. The square root of a number x {\displaystyle
Radical_symbol
Greatest integer less than or equal to square root
integer square root (isqrt) of a non-negative integer n is the non-negative integer m which is the greatest integer less than or equal to the square root of
Integer_square_root
Unique positive real number which when multiplied by itself gives 3
The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3. It is denoted mathematically as 3 {\textstyle {\sqrt
Square_root_of_3
Matrix B such that B² equals a given matrix A
mathematics, the square root of a matrix extends the notion of square root from numbers to matrices. A matrix B is said to be a square root of A if the matrix
Square_root_of_a_matrix
Square root of a non-positive real number
Alexandria is noted as the first to present a calculation involving the square root of a negative number, it was Rafael Bombelli who first set down the rules
Imaginary_number
Unique positive real number which when multiplied by itself gives 8
The square root of 8 is the positive real number that, when multiplied by itself, gives the natural number 8. It is more precisely called the principal
Square_root_of_8
Positive real number which when multiplied by itself gives 6
The square root of 6 is the positive real number that, when multiplied by itself, gives the natural number 6. It is more precisely called the principal
Square_root_of_6
Arithmetic operation, inverse of nth power
number x of which the root is taken is the radicand. A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree
Nth_root
Statistical measure
The root mean square deviation (RMSD) or root mean square error (RMSE) is a frequently used measure of the distances between actual observed values and
Root_mean_square_deviation
Positive real number which when multiplied by itself gives 5
The square root of 5, denoted 5 {\displaystyle {\sqrt {5}}} , is the positive real number that, when multiplied by itself, gives the natural number
Square_root_of_5
Formula for solving a quadratic equation
Because the left-hand side is now a perfect square, we can easily take the square root of both sides: x+b2a=±b2−4ac2a. Finally, subtracting b/2a
Quadratic_formula
Unofficial holiday
Square Root Day is an unofficial holiday celebrated on days when both the day of the month and the month are the square root of the last two digits of
Square_Root_Day
Natural number
non-trivial normal magic square, called the Luoshu square. All integers n≥34 can be expressed as the sum of five non-zero squares. There are five countably
5
Natural number
prime number, second smallest prime number, and the only prime preceding a square number. It has religious and cultural significance in many societies. The
3
Positive real number which when multiplied by itself gives 7
The square root of 7 is the positive real number that, when multiplied by itself, gives the prime number 7. It is an irrational algebraic number. The
Square_root_of_7
Specific probability distribution function, important in physics
with a scale parameter measuring speeds in units proportional to the square root of T / m {\displaystyle T/m} (the ratio of temperature and particle mass)
Maxwell–Boltzmann distribution
Maxwell–Boltzmann_distribution
Natural number
number, a square, a Motzkin number, and the number of derangements of 4 items. In the decimal system, 9 is the largest possible digital root. Casting out
9
Function that, applied twice, gives another function
In mathematics, a functional square root (sometimes called a half iterate) is a square root of a function with respect to the operation of function composition
Functional_square_root
Natural number
The chemical element with atomic number 2 is helium. Binary number Square root of 2 −2 Colman, Samuel (1912). Coan, C. Arthur (ed.). Nature's Harmonic
2
Natural number
and digit. It is the natural number following 3 and preceding 5. It is a square number, the smallest semiprime and composite number, and is considered unlucky
4
Problem of constructing equal-area shapes
Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a given
Squaring_the_circle
Polynomial with no repeated root
In mathematics, a square-free polynomial is a univariate polynomial (over a field or an integral domain) that has no multiple root in an algebraically
Square-free_polynomial
Removal of square roots from denominators
{\displaystyle {\sqrt[{n}]{x}}^{n-r}.} If the denominator is linear in some square root, say a + b x , {\displaystyle a+b{\sqrt {x}},} rationalisation consists
Rationalisation_(mathematics)
Product of an integer with itself
In the real number system, square numbers are non-negative. A non-negative integer is a square number when its square root is again an integer. For example
Square_number
Economic term to distinguish types of recessions
recoveries. The most commonly used terms are V-shaped (with variations of square-root shaped, and Nike-swoosh shaped), U-shaped, W-shaped (also known as a
Recession_shapes
Mathematical concept
their cardinality is at most countable; since on the other hand every square root of a prime number is a distinct quadratic irrational, and there are countably
Quadratic_irrational_number
Number, approximately 1.618
rational, then 2φ−1=5, the square root of 5, must also be rational. This is a contradiction, as the square roots of all non-square natural numbers are irrational
Golden_ratio
Mathematical concept
and so, invertible. The inverse function here is called the (positive) square root function and is denoted by x↦x. The following table shows several standard
Inverse_function
A square root of 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
Square root of a 2 by 2 matrix
Square_root_of_a_2_by_2_matrix
Automated theorem proofer
mortal(x). man(socrates). -mortal(socrates). end_of_list. A proof that the square root of 2 is irrational can be expressed this way: formulas(assumptions).
Prover9
Measure of the error of an estimator
square of the quantity being estimated. In an analogy to standard deviation, taking the square root of MSE yields the root-mean-square error or root-mean-square
Mean_squared_error
Fixed number that has received a name
encounter during pre-college education in many countries. The square root of 2, often known as root 2 or Pythagoras' constant, and written as √2, is the unique
Mathematical_constant
Natural number
27 (twenty-seven) is the natural number following 26 and preceding 28. Including the null-motif, there are 27 distinct hypergraph motifs. There are exactly
27_(number)
Integer that is a perfect square modulo some integer
efficiently. Generate a random number, square it modulo n, and have the efficient square root algorithm find a root. Repeat until it returns a number not
Quadratic_residue
Expression which is not assigned an interpretation
the field of real numbers, the square root of a negative number is undefined, as no real number exists which, when squared, equals a negative number. Mathematicians
Undefined_(mathematics)
Method of allocating voting weight by population
The Penrose method (or square-root method) is a method devised in 1946 by Professor Lionel Penrose for allocating the voting weights of delegations (possibly
Penrose_method
Specific values of a multivalued function
example is given by the square root function: every nonzero complex number has two square roots. The principal value of the square root of a positive real
Principal_value
Length of a line segment
The two squared formulas inside the square root give the areas of squares on the horizontal and vertical sides, and the outer square root converts the
Euclidean_distance
Used to count, measure, and label
real numbers such as the square root of 2 (2), and pi (π), and complex numbers which extend the real numbers with a square root of −1 (i), and its combinations
Number
Computational method
square root of the same value. The generalized math summary is: n = order of the squared polynomial being factored m = order of the extracted square root
Factorization_of_polynomials
Functions of complex quaternions
function, whose power series converges everywhere in the complex plane, the square root function, and the logarithm function. A quaternion Q can be written as
Biquaternion_functions
Number expressed in the base-2 numeral system
result. The process of taking a binary square root digit by digit is essentially the same as for a decimal square root but much simpler, due to the binary
Binary_number
Polynomial equation of degree two
Produce two linear equations by equating the square root of the left side with the positive and negative square roots of the right side. Solve each of the
Quadratic_equation
Number with a real and an imaginary part
nonzero real number, whether positive or negative, squares to a positive number, taking the square root of a negative number was historically considered
Complex_number
Argument that leads to a logical absurdity
contradiction, since no prime number divides 1. The classic proof that the square root of 2 is irrational is a refutation by contradiction. Indeed, we set out
Reductio_ad_absurdum
Change of the sign of a square root
conjugate expressions do not involve the square root anymore. This property is used for removing a square root from a denominator, by multiplying the numerator
Conjugate_(square_roots)
Measure of variation in statistics
set or probability distribution is the square root of its variance (the variance being the average of the squared deviations from the mean). A useful property
Standard_deviation
Problem in computer science
Turing run-time complexity of the square-root sum problem? More unsolved problems in computer science The square-root sum problem (SRS) is a computational
Square-root_sum_problem
Polynomial function of degree two
golden ratio 1 + 5 2 . {\displaystyle {\frac {1+{\sqrt {5}}}{2}}.} The square root of a univariate quadratic function gives rise to one of the four conic
Quadratic_function
Babylonian mathematical clay tablet
an accurate sexagesimal approximation to the square root of 2, the length of the diagonal of a unit square. This number is given to the equivalent of six
YBC_7289
Calculating method used in ancient China
cereal=4 dou 1 4 {\displaystyle {\frac {1}{4}}} Algorithm for extraction of square root was described in Jiuzhang suanshu and with minor difference in terminology
Rod_calculus
Negative integer two units from the origin in mathematics
{1}{4}}} . The square reciprocals of the first few natural numbers are: The square root of negative two, defined with the imaginary unit i {\displaystyle i}
−2
Generalization of signum function to matrices
(A)=A^{-1}{\sqrt {A^{2}}}} , where we use the matrix square root. If we apply the Babylonian method to compute the square root of the matrix A 2 {\displaystyle A^{2}}
Matrix_sign_function
Weighting technique in economics
more recent OECD publications. The household income is divided by the square root of household size. 1.0 for household of 1 1.414 for household of 2 1
Equivalisation
Insurance purchased by an insurance company
reinsurers in a given national market should be approximately equal to the square-root of the number of primary insurers active in the same market. Econometric
Reinsurance
Test statistic
dating and variance of unit weight in the context of weighted least squares. Its square root is called regression standard error, standard error of the regression
Reduced_chi-squared_statistic
Linear filter in the time domain
In signal processing, a root-raised-cosine filter (RRC), sometimes known as square-root-raised-cosine filter (SRRC), is frequently used as the transmit
Root-raised-cosine_filter
Property of a mathematical matrix
{1}{2}},} hence it is also called the positive square root of M . {\displaystyle M.} The non-negative square root should not be confused with other decompositions
Definite_matrix
Two-dimensional packing problem
to its square root. The precise asymptotic growth rate of the wasted space, even for half-integer side lengths, remains an open problem. Square packing
Square_packing
Number divisible only by 1 and itself
the square root of n. Any such integer dividing n evenly establishes n as composite; otherwise it is prime. Integers larger than the square root do
Prime_number
Polynomial equation of degree 3
formula for a double root involves a square root, and, in characteristic 3, the formula for a triple root involves a cube root. Gerolamo Cardano is credited
Cubic_equation
1617 device for calculating products and quotients
above, 6839925 is less than 11669900, so the root needs to be rounded up to 6840.0. To find the square root of a number that isn't an integer, say 54782
Napier's_bones
Statistical principle about ratio of effects to causes
is known as the square-root-of-the-sum-of-the-squares axiom. This states that the variation caused by the steepest slope must be squared, and then the result
Pareto_principle
Measure of distance between atoms of superimposed proteins
In bioinformatics, the root mean square deviation of atomic positions, or simply root mean square deviation (RMSD), is the measure of the average distance
Root mean square deviation of atomic positions
Root_mean_square_deviation_of_atomic_positions
IEEE standard for floating-point arithmetic
of underflow. See Fast inverse square root and Methods of computing square roots#Iterative methods for reciprocal square roots As an implementation limit
IEEE_754
American mathematician (1921–2005)
adjacency matrix is the square of the adjacency matrix of a tree. If a graph G is the square of a tree, then it has a unique tree square root Some vocabulary
Frank_Harary
Terminology in physics
context. A root-power quantity is a quantity such as voltage, current, sound pressure, electric field strength, speed, or charge density, the square of which
Power, root-power, and field quantities
Power,_root-power,_and_field_quantities
Bibliometric hypothesis
Price's law or Price's square root law is a bibliometric hypothesis proposed by Derek J. de Solla Price suggesting that in any scientific field, half
Price's_law
Mathematical functions
complex arguments, the inverse circular and hyperbolic functions, the square root, and the natural logarithm are all multi-valued functions.
Inverse_hyperbolic_functions
Algebraic operation on coordinate vectors
product is used for defining lengths (the length of a vector is the square root of the scalar product of the vector by itself) and angles (the cosine
Dot_product
Concept in political science
higher exponent, closer to a square-root law, and that the data's deviation from the cube root rule makes the cube root statistically inferior. In this
Cube_root_law
Number used to approximate the square root of 2
comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins 1/1, 3/2, 7/5, 17/12
Pell_number
Number whose cube is a given number
root of numbers having many digits in the Aryabhatiya (section 2.5). Methods of computing square roots List of polynomial topics Nth root Square root
Cube_root
Statistical property
statistic is the standard deviation of its sampling distribution. It is the square root of the variance of an estimator of a parameter, as in the standard error
Standard_error
Group of Vedic Sanskrit texts
several early mathematical results, including an approximation of the square root of 2 and the statement of the Pythagorean theorem. Baudhayana's Śrauta
Baudhayana_sutras
Graphical representation of the distribution of numerical data
⌈ n ⌉ {\displaystyle k=\lceil {\sqrt {n}}\rceil \,} which takes the square root of the number of data points in the sample and rounds to the next integer
Histogram
Mathematical expression with outer and inner radicals
a nested radical is a radical expression (one containing a square root sign, cube root sign, etc.) that contains (nests) another radical expression
Nested_radical
Mechanical analog computer
square root, it may be possible to read from a D scale to an R1 scale running from 1 to square root of 10 or to an R2 scale running from square root of
Slide_rule
Average of squared values of a sample
{\displaystyle E(X^{2})} is also called the mean square. The square root of a mean square is known as the root mean square (RMS or rms), and can be used as an estimate
Mean_square
Chinese mathematician
Chemla, Similarities between Chinese and Arabic mathematical writings I : Root extraction, Arabic Sci. Philos. 4 (2) (1994), 207-266. S Guo, Preliminary
Jia_Xian
Functional square root of an exponential
In mathematics, a half-exponential function is a functional square root of an exponential function. That is, a function f such that f composed with itself
Half-exponential_function
Indian mathematician (c. 598–c. 668)
square. [The result is] the middle [number]. 18.45. Whatever is the square-root of the rupas multiplied by the square [and] increased by the square of
Brahmagupta
First electronic general-purpose digital computer
controlled by a special divider/square-rooter unit to perform up to 40 division operations per second or three square root operations per second. The other
ENIAC
Square matrix with ones on the main diagonal and zeros elsewhere
independent. The principal square root of an identity matrix is itself, and this is its only positive-definite square root. However, every identity matrix
Identity_matrix
Number that is not a ratio of integers
the golden ratio φ, and the square root of two. In fact, all square roots of natural numbers, other than of perfect squares, are irrational. Like any real
Irrational_number
Measure of the deviation of position over time
relevant concept, the variance-related diameter (VRD), defined as twice the square root of MSD, is also used in studying the transportation and mixing phenomena
Mean_squared_displacement
Measure of change in a periodic variable
Doppler spectroscopy). Root mean square (RMS) amplitude is used especially in electrical engineering: the RMS is defined as the square root of the mean over
Amplitude
Babylonian clay tablet of numbers in Pythagorean triples
that if it is squared and 1 subtracted, the result has a rational square root also with a finite sexagesimal representation. This square root, in fact, equals
Plimpton_322
Physical law
distance by a factor of 1.4 (the square root of 2), and to double illumination, reduce the distance to 0.7 (square root of 1/2). When the illuminant is
Inverse-square_law
Figurate number
all other strategies". By analogy with the square root of x, one can define the (positive) triangular root of x as the number n such that Tn = x: n =
Triangular_number
Integer that is both a perfect square and a triangular number
{\displaystyle 1} to n {\displaystyle n} has a square root that is an integer. There are infinitely many square triangular numbers; the first few are: 0, 1
Square_triangular_number
Probabilistic primality test
polynomials). Here follows a more elementary proof. Suppose that x is a square root of 1 modulo n. Then: ( x − 1 ) ( x + 1 ) = x 2 − 1 ≡ 0 ( mod n ) . {\displaystyle
Miller–Rabin_primality_test
Geometric pattern used in art
Another triangular lattice form is common, with circle separation as the square root of 3 times their radius. Richard Kershner showed in 1939 that no arrangement
Overlapping_circles_grid
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