3:49

2:52

3:03

3:48

3:40

In mathematics, a square root of a number a is a number y such that y2 = a; in other words, a number y whose square (the result of multiplying the number by itself, or y⋅y) is a. For example, 4 and −4 are square roots of 16 because 42 = (−4)2 = 16.
Every nonnegative real number a has a unique nonnegative square root, called the principal square root, which is denoted by √a, where √ is called the radical sign or radix. For example, the principal square root of 9 is 3, which is denoted by √9 = 3, because 32 = 3 • 3 = 9 and 3 is nonnegative. The term (or number) whose square root is being considered is known as the radicand. The radicand is the number or expression underneath the radical sign, in this example 9.

### History

### Properties and uses

### Square roots of positive integers

### Computation

### Square roots of negative and complex numbers

### Square roots of matrices and operators

### In integral domains, including fields

### In rings in general

### Geometric construction of the square root