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  2. nth root - Wikipedia

    en.wikipedia.org/wiki/Nth_root

    n. th root. In mathematics, an nth root of a number x is a number r (the root) which, when raised to the power of the positive integer n, yields x: The integer n is called the index or degree, and the 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.

  3. Square root - Wikipedia

    en.wikipedia.org/wiki/Square_root

    Square root. Notation for the (principal) square root of x. For example, √ 25 = 5, since 25 = 5 ⋅ 5, or 52 (5 squared). In mathematics, a square root of a number x is a number y such that ; in other words, a number y whose square (the result of multiplying the number by itself, or ) is x. [ 1] For example, 4 and −4 are square roots of 16 ...

  4. Nested radical - Wikipedia

    en.wikipedia.org/wiki/Nested_radical

    Nested radical. In algebra, a nested radical is a radical expression (one containing a square root sign, cube root sign, etc.) that contains (nests) another radical expression. Examples include. which arises in discussing the regular pentagon, and more complicated ones such as.

  5. Methods of computing square roots - Wikipedia

    en.wikipedia.org/wiki/Methods_of_computing...

    A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...

  6. Exact trigonometric values - Wikipedia

    en.wikipedia.org/wiki/Exact_trigonometric_values

    The trigonometric functions of angles that are multiples of 15°, 18°, or 22.5° have simple algebraic values. These values are listed in the following table for angles from 0° to 45°. [ 1] In the table below, the label "Undefined" represents a ratio If the codomain of the trigonometric functions is taken to be the real numbers these entries ...

  7. Clearing denominators - Wikipedia

    en.wikipedia.org/wiki/Clearing_denominators

    Clearing denominators. In mathematics, the method of clearing denominators, also called clearing fractions, is a technique for simplifying an equation equating two expressions that each are a sum of rational expressions – which includes simple fractions .

  8. Rationalisation (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Rationalisation_(mathematics)

    Rationalisation (mathematics) In elementary algebra, root rationalisation is a process by which radicals in the denominator of an algebraic fraction are eliminated. If the denominator is a monomial in some radical, say with k < n, rationalisation consists of multiplying the numerator and the denominator by and replacing by x (this is allowed ...

  9. Square root of a matrix - Wikipedia

    en.wikipedia.org/wiki/Square_root_of_a_matrix

    An n×n matrix with n distinct nonzero eigenvalues has 2 n square roots. Such a matrix, A, has an eigendecomposition VDV−1 where V is the matrix whose columns are eigenvectors of A and D is the diagonal matrix whose diagonal elements are the corresponding n eigenvalues λi. Thus the square roots of A are given by VD1/2 V−1, where D1/2 is ...

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