In mathematics, the number k is a square root of the number n if k2 = n. For example, 4 and –4 are the square roots of 16 since × 4= 16 and (–4)× (–4) = 16. The square root symbol is and for n greater than zero, the symbol is understood to be a positive number. Thus and
As further examples, the square root of 1 equals 1; the square root of 4 is 2; and the square root of 9 is 3. The other positive integers between 2 and 9 have much more complicated square roots.
Historically, the calculations for square roots were found in the Rhind Mathematical Papyrus (c. fifteenth century BC). Hundreds of years later (somewhere between 900 and 400 BC), ancient Indian mathematicians used square roots in their work. Modern usage of the square root sign was found in Europe in the sixteenth century. Mathematical historians claim that the symbol is a modified version of the Latin radix, which means root.
When n is a negative number, the square root is called imaginary. Customarily, is designated by i so that the square root of any negative number can be expressed as ai where a is a real number. Thus .
See also Imaginary number.