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Abū Kāmil Shujā ibn Aslam (Egypt, 10th century) in particular was the first to accept irrational numbers (often in the form of a square root, cube root or fourth root) as solutions to quadratic equations or as coefficients in an equation. [30] The 9th century Indian mathematician Sridhara wrote down rules for solving quadratic equations. [31]
In the physics of gas molecules, the root-mean-square speed is defined as the square root of the average squared-speed. The RMS speed of an ideal gas is calculated using the following equation: v RMS = 3 R T M {\displaystyle v_{\text{RMS}}={\sqrt {3RT \over M}}}
The numbered squares are referred to as primary square or root square if they are filled with primary numbers or root numbers, respectively. The numbers are placed about the skew diagonal in the root square such that the middle column of the resulting root square has 0, 5, 10, 15, 20 (from bottom to top).
The space diagonal of the unit cube is √ 3. Distances between vertices of a double unit cube are square roots of the first six natural numbers, including the square root of 3 (√7 is not possible due to Legendre's three-square theorem) This projection of the Bilinski dodecahedron is a rhombus with diagonal ratio √ 3.
The first of these two, 1;24,51,10 represents the number 305470/216000 ≈ 1.414213, a numerical approximation of the square root of two that is off by less than one part in two million. The second of the two numbers is 42;25,35 = 30547/720 ≈ 42.426.
One can prove [citation needed] that = is the largest possible number for which the stopping criterion | + | < ensures ⌊ + ⌋ = ⌊ ⌋ in the algorithm above.. In implementations which use number formats that cannot represent all rational numbers exactly (for example, floating point), a stopping constant less than 1 should be used to protect against round-off errors.
Hensel's original lemma concerns the relation between polynomial factorization over the integers and over the integers modulo a prime number p and its powers. It can be straightforwardly extended to the case where the integers are replaced by any commutative ring, and p is replaced by any maximal ideal (indeed, the maximal ideals of have the form , where p is a prime number).
The English language uses many Greek and Latin roots, stems, and prefixes. These roots are listed alphabetically on three pages: Greek and Latin roots from A to G; Greek and Latin roots from H to O; Greek and Latin roots from P to Z. Some of those used in medicine and medical technology are listed in the List of medical roots, suffixes and ...
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