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  2. 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 ...

  3. Functional square root - Wikipedia

    en.wikipedia.org/wiki/Functional_square_root

    Notations expressing that f is a functional square root of g are f = g [1/2] and f = g 1/2 [citation needed] [dubious – discuss], or rather f = g 1/2 (see Iterated function#Fractional_iterates_and_flows,_and_negative_iterates), although this leaves the usual ambiguity with taking the function to that power in the multiplicative sense, just as f ² = f ∘ f can be misinterpreted as x ↦ f(x)².

  4. Kunerth's algorithm - Wikipedia

    en.wikipedia.org/wiki/Kunerth's_algorithm

    It is quite easy to choose X and Y such that (+) / is a square. The modular square root of 67 y mod R S A 260 {\displaystyle {\sqrt {67y}}{\bmod {RSA260}}} can be taken this way. Having solved the associated quadratic equation we now have the variables w and set v = r (if C in the quadratic is a natural square).

  5. Solution in radicals - Wikipedia

    en.wikipedia.org/wiki/Solution_in_radicals

    A solution in radicals or algebraic solution is an expression of a solution of a polynomial equation that is algebraic, that is, relies only on addition, subtraction, multiplication, division, raising to integer powers, and extraction of n th roots (square roots, cube roots, etc.). A well-known example is the quadratic formula

  6. Square root - Wikipedia

    en.wikipedia.org/wiki/Square_root

    The square root of a positive integer is the product of the roots of its prime factors, because the square root of a product is the product of the square roots of the factors. Since p 2 k = p k , {\textstyle {\sqrt {p^{2k}}}=p^{k},} only roots of those primes having an odd power in the factorization are necessary.

  7. Laguerre's method - Wikipedia

    en.wikipedia.org/wiki/Laguerre's_method

    Laguerre's method may even converge to a complex root of the polynomial, because the radicand of the square root may be of a negative number, in the formula for the correction, , given above – manageable so long as complex numbers can be conveniently accommodated for the calculation. This may be considered an advantage or a liability ...

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