
Review of Short Phrases and Links 
This Review contains major "Square Root" related terms, short phrases and links grouped together in the form of Encyclopedia article.
Definitions
 Square root is a factor of a number that yields the number when it is squared.
 Square root is a costly calculation, and it would have to do it for every polygon.
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 Since the square root is a concave function, it follows from Jensen's inequality that the square root of the sample variance is an underestimate.
 Now, in that same section, it will say "For a side length of ." The truncated tetrahedron, for example, will have "the square root of 8".
 Since the variance of each effect is shown in the diagram as an area, the square root of the area represents the standard deviation of that effect.
 The standard deviation of the counts in the repeated experiments should be close to the square root of 1000 (31.6).
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 But Bhaskara did correctly find out that the square of zero is zero, as is the square root.
 The square root of σ 2 is called the standard deviation and is the width of the density function.
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 The eruption velocity, Uv, is nearly proportional to the square root of temperature.
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 We've already seen this in the case where we throw in a square root of n, or an nth root of 1.
 One way for this to happen is if the quantity in the square root is a perfect square.
 Root Mean Square Percentage Error: Square root of the average sum of squared errors expressed as a percentage.
 The thermal energy can be used to calculate the root mean square speed of the atoms, which is inversely proportional to the square root of the atomic mass.
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 To compensate, we simply divide this Pythagorean distance result by the square root of the dimension.
 Grover showed in 1996 a quantum algorithm to search unsorted databases in the square root of the time it would take a classical computer to find an entry.
 This problem can be solved by working with the square root of the variance, which is called the standard deviation.
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 So f is the square root of an analytic function, and hence f has a removable singularity at 0, or has 0 as a branch point.
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 Facts about the exchange matrix J: J is a square root of the identity matrix; J is a permutation.
 The root mean squared error (RMSE) (or root mean squared deviation (RMSD)) is then simply defined as the square root of the MSE.
 To avoid making such mistakes when manipulating complex numbers, a strategy is never to use a negative number under a square root sign.
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 For every nonzero complex number z there exist precisely two numbers w such that w 2 = z: the principal square root of z (defined below), and its negative.
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 Excerpted from Imagining Numbers: (particularly the square root of minus fifteen) by Barry Mazur.
 In fact, the above procedure may be used to find the square root and cubic root of a matrix.
 They use an abacus to perform the mathematical functions multiplication, division, addition, subtraction, square root and cubic root.
 This function returns the square root of the corresponding variance function above.
 The negative square root solution outside the horizon represents another Universe.
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 When the spin c structure is nonzero this square root bundle has a nonintegral Chern class, which means that it fails the triple overlap condition.
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 So, the standard deviation is the square root of five halves, or approximately 1.58.
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 The square root of the variance, the standard deviation σ is.
 Standard Deviation: The standard deviation is the square root of the average squared deviation from the mean.
 The principal square root function is thus defined using the nonpositive real axis as a branch cut.
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 The standard deviation is the square root of the variance, bringing the measure back to scale (and prompting its other name of rootmeansquare; see r.m.s.
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 This is the standardized residual value (observed minus predicted divided by the square root of the residual mean square).
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 The square root of the arithmetic mean of the squares of a set of numbers is called their rootmeansquare.
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 The principal square root function is holomorphic everywhere except on the set of nonpositive real numbers (where it isn't even continuous).
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 Let A=AFILE, B=BFILE. The elements of matrix B are simply equal to the square root of the elements of matrix A. B[i,j] = SQRT(A[i,j]).
 For positive real numbers, the principal root is simply the positive square root.
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 What types of functions don't have an inverse, like square root functions, exponential functions, cubic functions, etc.
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 The square root function also maps the area of a square to its side length.
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 The square root function can be defined as sqrt{z} = e^{frac{1}{2}log z} and is therefore holomorphic wherever the logarithm log(z) is.
 For example, just as the square root function is defined such that y 2 = x, the function y = arcsin(x) is defined so that sin(y) = x.
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 The square root of this parameter is given a special name, the standard error.
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 However very often we instead quote the standard deviation of the variable, which is the square root of its variance, or root mean square deviation.
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 Formula: The square root of (the moment of inertia in inches^4 divided by the area of the section in inches^2) expressed in inches.
 By analogy with RMS voltage and RMS current, RMS power is the square root of the mean of the square of the power over some specified time period.
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 Range reduction involves isolating the power of two of the argument and using a polynomial approximation to obtain a rough value for the square root.
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 The standard deviation is often denoted by the symbol s and is the square root of the variance.
 Since the speed of sound in gases increases with the square root of temperature, the use of hot exhaust gas greatly improves performance.
 The twilight factor is just a calculation which is the square root of the objective diameter time the power.
 Mathematicians have extended this concept to include abstractions such as the square root of minus one.
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 The approximation of the square root of 2 is four sexagesimal figures, which is about six decimal figures.
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 In three dimensions the distance from (0,0,0) to a point one away in each dimension is the square root of three.
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 As a consequence of this point of view, spinors may be regarded as a kind of "square root" of isotropic vectors.
 The only way of finding one is to divide by every integer lower than the square root of it.
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 Hence the rate of change is proportional to the square root of the semimajor axis to the third power divided by the factor (1 eccentricity squared).
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 An aircraft’s stall speed increases by a factor of the square root of the secant of the angle of bank, all other things being equal.
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 He speculates that the observed long range electric charge is smaller than the core electron charge by a factor of the square root of 137, ie 11.7.
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Categories
 Information > Evaluation > Analysis > Standard Deviation
 Information > Evaluation > Analysis > Variance
 Irrational
 Squares
 Standard Error
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