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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. 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.

  4. Closed-form expression - Wikipedia

    en.wikipedia.org/wiki/Closed-form_expression

    The quadratic formula =. is a closed form of the solutions to the general quadratic equation + + =. More generally, in the context of polynomial equations, a closed form of a solution is a solution in radicals; that is, a closed-form expression for which the allowed functions are only n th-roots and field operations (+,,, /).

  5. 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.

  6. nth root - Wikipedia

    en.wikipedia.org/wiki/Nth_root

    A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred by using ordinal numbers, as in fourth root, twentieth root, etc. The computation of an n th root is a root extraction. For example, 3 is a square root of 9, since 3 2 = 9, and −3 is also a square root of 9, since (−3) 2 = 9.

  7. Radical symbol - Wikipedia

    en.wikipedia.org/wiki/Radical_symbol

    The radical symbol refers to the principal value of the square root function called the principal square root, which is the positive one. 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.

  8. Square root of 5 - Wikipedia

    en.wikipedia.org/wiki/Square_root_of_5

    The approximation ⁠ 161 / 72 ⁠ (≈ 2.23611) for the square root of five can be used. Despite having a denominator of only 72, it differs from the correct value by less than ⁠ 1 / 10,000 ⁠ (approx. 4.3 × 10 −5). As of January 2022, the numerical value in decimal of the square root of 5 has been computed to at least 2,250,000,000,000 ...

  9. Expression (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Expression_(mathematics)

    A formal expression is a kind of string of symbols, created by the same production rules as standard expressions, however, they are used without regard to the meaning of the expression. In this way, two formal expressions are considered equal only if they are syntactically equal, that is, if they are the exact same expression.