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Number whose square is a given number
mathematics, a square root of 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
Square_root
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
Algorithms for calculating square roots
Square root algorithms compute the non-negative square root S {\displaystyle {\sqrt {S}}} of a positive real number S {\displaystyle S} . Since all square
Square_root_algorithms
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
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
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
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
Principal square root of minus 1
distinct complex-valued square roots, which are additive inverses of each other, while zero has only zero as its (double) square root. Historically, the imaginary
Imaginary_unit
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
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
Mathematical operation
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
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
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
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
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
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
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
normal magic square, called the Luoshu square. All integers n ≥ 34 {\displaystyle n\geq 34} can be expressed as the sum of five non-zero squares. There are
5
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 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
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
Formula that provides the solutions to a quadratic equation
\end{aligned}}} Because the left-hand side is now a perfect square, we can easily take the square root of both sides: x + b 2 a = ± b 2 − 4 a c 2 a . {\displaystyle
Quadratic_formula
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
Natural number
but some VFD models use the latter. 9 is the fourth composite number, a square, a Motzkin number, and the number of derangements of 4 items. Casting out
9
Problem of constructing equal-area shapes
) is a transcendental number. That is, π {\displaystyle \pi } is not the root of any polynomial with rational coefficients. It had been known for decades
Squaring_the_circle
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
4, and is the smallest odd prime number and the only prime preceding a square number. It has religious and cultural significance in many societies. The
3
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)
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
Number, approximately 1.618
{5}}} , the square root of 5 {\displaystyle 5} , must also be rational. This is a contradiction, as the square roots of all non-square natural numbers
Golden_ratio
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
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
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
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
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
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
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
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
Used to count, measure, and label
the square root of 2 ( 2 ) {\displaystyle \left({\sqrt {2}}\right)} , and pi (π), and complex numbers which extend the real numbers with a square root of
Number
Law of voting power distribution
In the mathematical theory of games, the Penrose square root law, originally formulated by Lionel Penrose, concerns the distribution of the voting power
Penrose_square_root_law
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
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
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
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
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
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)
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
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
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 concept
and so, invertible. The inverse function here is called the (positive) square root function and is denoted by x ↦ x {\displaystyle x\mapsto {\sqrt {x}}}
Inverse_function
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
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
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
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
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
Arithmetic operation
_{y}x} Like square roots, the square super-root of x may not have a single solution. Unlike square roots, determining the number of square super-roots
Tetration
Square root biased sampling is a sampling method proposed by William H. Press, a computer scientist and computational biologist, for use in airport screenings
Square_root_biased_sampling
American actor (born 1969)
no effect. One times one equals two because the square root of four is two, so what's the square root of two? Should be one, but we're told it's two,
Terrence_Howard
Four-dimensional number system
The norm of a quaternion (the square root of the product with its conjugate, as with complex numbers) is the square root of the determinant of the corresponding
Quaternion
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
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
{\displaystyle P(A\mid B)} : see "|". √ (square-root symbol) Denotes square root and is read as the square root of. Rarely used in modern mathematics without
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
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
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
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
Number divisible only by 1 and itself
Eratosthenes can be sped up by considering only the prime divisors up to the square root of the upper limit. Fibonacci took the innovations from Islamic mathematics
Prime_number
Portion of a solid that lies between two parallel planes cutting the solid
deriving this formula, and with it, encountering the imaginary unit: the square root of negative one. In particular: The volume of a circular cone frustum
Frustum
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
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
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
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
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
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
First electronic general-purpose digital computer
included Robert F. Shaw (function tables), Jeffrey Chuan Chu (divider/square-rooter), Thomas Kite Sharpless (master programmer), Frank Mural (master programmer)
ENIAC
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
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
Algorithm that estimates unknowns from a series of measurements over time
yk. The l·d·lt square-root filter requires orthogonalization of the observation vector. This may be done with the inverse square-root of the covariance
Kalman_filter
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
Basic concepts of algebra
an operation of arity one that has only one operand; for example, the square root. An example of a ternary operation (arity three) is the triple product
Elementary_algebra
Audible vibration that travels via pressure waves in matter
usually averaged over time and/or space, and a square root of this average provides a root mean square (RMS) value. For example, 1 Pa RMS sound pressure (94
Sound
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
Number representing a continuous quantity
square root of 2, is Cauchy but it does not converge to a rational number (in the real numbers, in contrast, it converges to the positive square root
Real_number
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 all real
Irrational_number
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
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
Association of one output to each input
the domain of the square root function, along a path of complex numbers with positive imaginary parts, one gets i for the square root of −1; while, when
Function_(mathematics)
Indian mathematician and astronomer (598–668)
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
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
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
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 whose cube is a given number
In mathematics, a cube root of a number x is a number y that has the given number as its third power; that is y 3 = x . {\displaystyle y^{3}=x.} The number
Cube_root
Method of drawing geometric objects
closed under the complex conjugate and square root operations (to avoid ambiguity, we can specify the square root with complex argument less than π). The
Straightedge and compass construction
Straightedge_and_compass_construction
Statistical measure of how far values spread from their average
the expected value of the squared deviation from the mean of a random variable. The standard deviation is the square root of the variance. Technically
Variance
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
Ancient algorithm for generating prime numbers
optimal trial division algorithm uses all prime numbers not exceeding its square root, whereas the sieve of Eratosthenes produces each composite from its prime
Sieve_of_Eratosthenes
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)
Shape with four equal sides and angles
term squaring to mean raising any number to the second power. Reversing this relation, the side length of a square of a given area is the square root of
Square
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
Polynomial function of degree 4
square root of α and that r3 + r4 is the other square root of α. For the same reason, r1 + r3 is a square root of β, r2 + r4 is the other square root
Quartic_function
Product of a number by itself
number whose square is the original number. No square root can be taken of a negative number within the system of real numbers, because squares of all real
Square_(algebra)
SQUARE ROOT
SQUARE ROOT
Surname or Lastname
English
English : variant of Spear.
Boy/Male
English American
Shieldbearer.
Male
Swedish
Swedish name derived from Old Norse stúra, STURE means "obstinate."
Boy/Male
British, English
Spear-man
Boy/Male
French Latin
A squire.
Surname or Lastname
English
English : status name from Middle English squyer ‘esquire’, ‘a man belonging to the feudal rank immediately below that of knight’ (from Old French esquier ‘shield bearer’). At first it denoted a young man of good birth attendant on a knight, or by extension any attendant or servant, but by the 14th century the meaning had been generalized, and referred to social status rather than age. By the 17th century, the term denoted any member of the landed gentry, but this is unlikely to have influenced the development of the surname.
Boy/Male
Indian
Cover
Male
English
French form of English Stewart, STUART means "house guard; steward." In use by the English and Scottish.
Boy/Male
Italian
Squire.
Girl/Female
British, English
Bless
Boy/Male
American, Australian, British, English
Shield Bearer; Knight's Companion
Boy/Male
American, Anglo, Australian, British, Chinese, Christian, Danish, English, French, German, Scottish
Steward; Stewart is Clan Name of the Royal House of Scotland; Surname; House Guard
Boy/Male
American, British, English
Shield Bearer
Boy/Male
English
Shieldbearer.
Boy/Male
Anglo Saxon American English Scottish
Steward.
Surname or Lastname
English
English : patronymic from Squire.
Surname or Lastname
English
English : variant of Squire.
Surname or Lastname
English
English : patronymic from Squire.
Male
Chinese
square, in the sense of correctness.
Surname or Lastname
English
English : nickname for a frugal person, from Middle English spare ‘sparing’, ‘frugal’.
SQUARE ROOT
SQUARE ROOT
Boy/Male
Hindu
Surname or Lastname
English
English : variant of Gillings.
Boy/Male
Tamil
Steady
Surname or Lastname
English (West Midlands)
English (West Midlands) : from Middle English schovel ‘shovel’, hence a metonymic occupational name for a maker or seller of shovels, or for someone who regularly used a shovel in his work.
Girl/Female
Muslim
Cone bearing tree
Boy/Male
Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Mythological, Telugu
A Yaksha King
Boy/Male
Australian, Czech, Czechoslovakian, Slavic
Fortress
Girl/Female
Biblical
A song of trouble or comfort.
Boy/Male
Hindu
A part of a Moon
Girl/Female
Australian, British, Christian, English
Merciful; Variant of Clementia Used as a Virtue Name by the Puritans
SQUARE ROOT
SQUARE ROOT
SQUARE ROOT
SQUARE ROOT
SQUARE ROOT
n.
Hence, anything which is square, or nearly so
n.
To form with right angles and straight lines, or flat surfaces; as, to square mason's work.
a.
Having four equal sides and four right angles; as, a square figure.
n.
To make even, so as leave no remainder of difference; to balance; as, to square accounts.
n.
To multiply by itself; as, to square a number or a quantity.
n.
A square piece or fragment.
n.
To place at right angles with the keel; as, to square the yards.
n.
Having the toe square.
n.
One who, or that which, squares.
a.
Rendering equal justice; exact; fair; honest, as square dealing.
n.
A square; a measure; a rule.
a.
Forming a right angle; as, a square corner.
n.
The product of a number or quantity multiplied by itself; thus, 64 is the square of 8, for 8 / 8 = 64; the square of a + b is a2 + 2ab + b2.
imp. & p. p.
of Square
n.
An instrument having at least one right angle and two or more straight edges, used to lay out or test square work. It is of several forms, as the T square, the carpenter's square, the try-square., etc.
a.
Even; leaving no balance; as, to make or leave the accounts square.
a.
Of or pertaining to a square, or to squares; resembling a quadrate, or square; square.
v. t.
To attend as a squire.
imp. & p. p.
of Squire
n.
A square. See 1st Squire.