If is a magma, such as a monoid, (which we write multiplicatively) and is an element of , then the element is the square of . Conversely, if , then is a square root of . If is an integral domain, then (in classical mathematics) and are the only square roots of . If has a square root, then we often denote its square roots together as , although there is no meaning of itself. If is a linearly ordered field, then every element has a unique nonnegative square root if it has a square root at all;...