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  2. 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.

  3. 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 ...

  4. 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 ...

  5. Radical symbol - Wikipedia

    en.wikipedia.org/wiki/Radical_symbol

    The two square roots of a negative number are both imaginary numbers, and the square root symbol refers to the principal square root, the one with a positive imaginary part. For the definition of the principal square root of other complex numbers, see Square root § Principal square root of a complex number.

  6. 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.

  7. Trump complains that US flags will be half-staff on his ...

    www.aol.com/news/trump-complains-us-flags-half...

    President-elect Donald Trump complained on Friday that American flags would still be lowered to half-staff in honor of the late President Jimmy Carter during Trump's Jan. 20 inauguration.

  8. American ski racer Lindsey Vonn is picking up speed in her ...

    www.aol.com/american-ski-racer-lindsey-vonn...

    Word on the mountain has it that Lindsey Vonn is still fast through a downhill course, even at 40 years old. On a frigid Friday morning, Vonn darted through the shadows along the speed course at ...

  9. Weather to keep planes carrying protest banners away from ...

    www.aol.com/sports/weather-keep-planes-carrying...

    The skies above MetLife Stadium may feature clouds and rain for Sunday's New York Giants home finale against the Indianapolis Colts — they won't, however, have any planes carrying protest banners.