## square root function

### The square root function, denoted by √x or sqrt(x), is a mathematical function that gives the non-negative square root of a number

The square root function, denoted by √x or sqrt(x), is a mathematical function that gives the non-negative square root of a number. It is an inverse function of squaring and is defined for non-negative real numbers.

The square root function can be described as follows:

For any non-negative real number x, the square root function √x returns a value y such that y^2 = x. In other words, if y = √x, then y squared (y^2) equals x.

For example, if we take x = 16, the square root function would give us y = 4, since 4 squared (4^2) equals 16. So, in this case, √16 = 4.

It is important to note that the square root function only gives the principal square root, which is the positive square root. For example, √4 = 2, not -2.

The square root function has several properties:

1. Domain: The domain of the square root function is all non-negative real numbers, [0, ∞).

2. Range: The range is also all non-negative real numbers, [0, ∞).

3. Graph: The graph of the square root function is a curve that starts at the point (0, 0) and increases gradually.

4. Even function: The square root function is an even function, which means it is symmetric about the y-axis. For example, √x = √(-x) for any x in its domain.

5. Inverse of squaring: The square root function is the inverse of squaring, meaning if you square a number and then take its square root, you will get back the original number.

6. Not defined for negative numbers: The square root function is not defined for negative real numbers. The square root of a negative number yields a complex number, which lies outside the domain of the square root function.

Overall, the square root function is widely used in various mathematical applications, such as finding the side lengths of squares, determining solutions of quadratic equations, and calculating distances in geometry and physics.

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