The square root of a number which is written as , is the positive number that when multiplied by itself equals Below is an example. Square roots and raising a number to the nd power are operations that undo each other.
The square root as an object and as a process are consider distinct mathematical ideas. As an object, a square root is always positive. For instance, because this refers to the principle root of has been established. This convention removes all ambiguity. However, the square root as an operation takes both positive and negative values. Consider the equation To solve for the square root of both sides of the equation must be taken. The values of that make the above equation true are and because
The square root of a negative number cannot be a real number. This is because there is no real number that exists such that when it is multiplied by itself, a negative value is produced. Instead, the square roots of negative numbers produce imaginary numbers.