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  2. Square root - Wikipedia

    en.wikipedia.org/wiki/Square_root

    The square root of a positive number is usually defined as the side length of a square with the area equal to the given number. But the square shape is not necessary for it: if one of two similar planar Euclidean objects has the area a times greater than another, then the ratio of their linear sizes is .

  3. 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 ...

  4. nth root - Wikipedia

    en.wikipedia.org/wiki/Nth_root

    A square root of a number x is a number r which, when squared, becomes x: =. Every positive real number has two square roots, one positive and one negative. For example, the two square roots of 25 are 5 and −5. The positive square root is also known as the principal square root, and is denoted with a radical sign:

  5. Integer square root - Wikipedia

    en.wikipedia.org/wiki/Integer_square_root

    In number theory, the integer square root (isqrt) of a non-negative integer n is the non-negative integer m which is the greatest integer less than or equal to the square root of n, ⁡ = ⌊ ⌋. For example, isqrt ⁡ ( 27 ) = ⌊ 27 ⌋ = ⌊ 5.19615242270663... ⌋ = 5. {\displaystyle \operatorname {isqrt} (27)=\lfloor {\sqrt {27}}\rfloor ...

  6. Algebraic number - Wikipedia

    en.wikipedia.org/wiki/Algebraic_number

    An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, (+) /, is an algebraic number, because it is a root of the polynomial x 2 − x − 1. That is, it is a value for x for which the polynomial evaluates to zero.

  7. Positive real numbers - Wikipedia

    en.wikipedia.org/wiki/Positive_real_numbers

    The division function takes a value of one when numerator and denominator are equal. Other ratios are compared to one by logarithms, often common logarithm using base 10. The ratio scale then segments by orders of magnitude used in science and technology, expressed in various units of measurement.

  8. Mathematical fallacy - Wikipedia

    en.wikipedia.org/wiki/Mathematical_fallacy

    The square root is multivalued. One value can be chosen by convention as the principal value; in the case of the square root the non-negative value is the principal value, but there is no guarantee that the square root given as the principal value of the square of a number will be equal to the original number (e.g. the principal square root of ...

  9. AM–GM inequality - Wikipedia

    en.wikipedia.org/wiki/AM–GM_inequality

    In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list; and further, that the two means are equal if and only if every number in the list is the same (in which ...