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Notation for the (principal) square root of x. For example, √ 25 = 5, since 25 = 5 ⋅ 5, or 5 2 (5 squared). In mathematics, a square root of a number x is a number y such that =; in other words, a number y whose square (the result of multiplying the number by itself, or ) is x. [1]
It includes all quadratic irrational roots, all rational numbers, and all numbers that can be formed from these using the basic arithmetic operations and the extraction of square roots. (By designating cardinal directions for +1, −1, + i , and − i , complex numbers such as 3 + i 2 {\displaystyle 3+i{\sqrt {2}}} are considered constructible.)
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 ...
Square root of 3, Theodorus' constant ... Real root of = 46 to 120 CE [11] Cube root of 3 1.44224 95703 ... For almost all real numbers x, ...
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 ...
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.
A solution in radicals or algebraic solution is an expression of a solution of a polynomial equation that is algebraic, that is, relies only on addition, subtraction, multiplication, division, raising to integer powers, and extraction of n th roots (square roots, cube roots, etc.). A well-known example is the quadratic formula
The extraction of decimal-fraction approximations to square roots by various methods has used the square root of 7 as an example or exercise in textbooks, for hundreds of years. Different numbers of digits after the decimal point are shown: 5 in 1773 [ 4 ] and 1852, [ 5 ] 3 in 1835, [ 6 ] 6 in 1808, [ 7 ] and 7 in 1797. [ 8 ]