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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. 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.

  4. Proof by infinite descent - Wikipedia

    en.wikipedia.org/wiki/Proof_by_infinite_descent

    In mathematics, a proof by infinite descent, also known as Fermat's method of descent, is a particular kind of proof by contradiction [1] used to show that a statement cannot possibly hold for any number, by showing that if the statement were to hold for a number, then the same would be true for a smaller number, leading to an infinite descent and ultimately a contradiction. [2]

  5. Nested radical - Wikipedia

    en.wikipedia.org/wiki/Nested_radical

    In the case of two nested square roots, the following theorem completely solves the problem of denesting. [2]If a and c are rational numbers and c is not the square of a rational number, there are two rational numbers x and y such that + = if and only if is the square of a rational number d.

  6. Pell number - Wikipedia

    en.wikipedia.org/wiki/Pell_number

    The Pell numbers are defined by the recurrence relation: = {=; =; + In words, the sequence of Pell numbers starts with 0 and 1, and then each Pell number is the sum of twice the previous Pell number, plus the Pell number before that.

  7. Pell's equation - Wikipedia

    en.wikipedia.org/wiki/Pell's_equation

    These solutions may be used to accurately approximate the square root of n by rational numbers of the form x/y. This equation was first studied extensively in India starting with Brahmagupta , [ 1 ] who found an integer solution to 92 x 2 + 1 = y 2 {\displaystyle 92x^{2}+1=y^{2}} in his Brāhmasphuṭasiddhānta circa 628. [ 2 ]

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  9. Talk:Darcy friction factor formulae - Wikipedia

    en.wikipedia.org/wiki/Talk:Darcy_friction_factor...

    The Colebrook Equation and the Haaland's solution are written for 1/sqrt(f) rather than for 'f' and this is IMHO the right thing to do. However the Swamee-Jain and Serghide's solutions are written for 'f' instead of 1/sqrt(f) which makes them inconsistent with the first two equations and makes them more difficult to understand.

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