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  2. Methods of computing square roots - Wikipedia

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

    From the multiplication tables, the square root of the mantissa must be 8 point something because a is between 8×8 = 64 and 9×9 = 81, so k is 8; something is the decimal representation of R. The fraction R is 75 − k 2 = 11, the numerator, and 81 − k 2 = 17, the denominator. 11/17 is a little less than 12/18 = 2/3 = .67, so guess .66 (it's ...

  3. Square root of 2 - Wikipedia

    en.wikipedia.org/wiki/Square_root_of_2

    The square root of two is the frequency ratio of a tritone interval in twelve-tone equal temperament music. The square root of two forms the relationship of f-stops in photographic lenses, which in turn means that the ratio of areas between two successive apertures is 2.

  4. Integer square root - Wikipedia

    en.wikipedia.org/wiki/Integer_square_root

    /// Performs a Karatsuba square root on a `u64`. pub fn u64_isqrt (mut n: u64)-> u64 {if n <= u32:: MAX as u64 {// If `n` fits in a `u32`, let the `u32` function handle it. return u32_isqrt (n as u32) as u64;} else {// The normalization shift satisfies the Karatsuba square root // algorithm precondition "a₃ ≥ b/4" where a₃ is the most ...

  5. Quadratic equation - Wikipedia

    en.wikipedia.org/wiki/Quadratic_equation

    Figure 1. Plots of quadratic function y = ax 2 + bx + c, varying each coefficient separately while the other coefficients are fixed (at values a = 1, b = 0, c = 0). A quadratic equation whose coefficients are real numbers can have either zero, one, or two distinct real-valued solutions, also called roots.

  6. Cube root - Wikipedia

    en.wikipedia.org/wiki/Cube_root

    This means that in polar coordinates, we are taking the cube root of the radius and dividing the polar angle by three in order to define a cube root. With this definition, the principal cube root of a negative number is a complex number, and for instance − 8 3 {\displaystyle {\sqrt[{3}]{-8}}} will not be −2, but rather 1 + i 3 ...

  7. Cubic equation - Wikipedia

    en.wikipedia.org/wiki/Cubic_equation

    Here ⁡ is an angle in the unit circle; taking ⁠ 1 / 3 ⁠ of that angle corresponds to taking a cube root of a complex number; adding −k ⁠ 2 π / 3 ⁠ for k = 1, 2 finds the other cube roots; and multiplying the cosines of these resulting angles by corrects for scale.

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