The Square Root Function | Definition, Properties, and Applications

square root function

The square root function is a mathematical function that takes a non-negative number as an input and returns the non-negative number whose square is equal to the input

The square root function is a mathematical function that takes a non-negative number as an input and returns the non-negative number whose square is equal to the input. It is denoted as √x or sqrt(x).

The square root function can be defined formally as follows:
For any non-negative real number x, the square root of x, denoted as √x or sqrt(x), is the non-negative real number y such that y^2 = x.

For example, if we want to calculate the square root of 16, we can write it as √16 or sqrt(16). The square root of 16 is 4 since 4^2 = 16.

The square root function has several important properties:
1. Non-negativity: The output of the square root function is always non-negative.
2. Principal square root: For positive real numbers, the square root function gives a unique positive value.
3. Multiplication: The square root of the product of two numbers is equal to the product of their square roots. For example, sqrt(a * b) = sqrt(a) * sqrt(b).
4. Division: The square root of the ratio of two numbers is equal to the ratio of their square roots. For example, sqrt(a / b) = sqrt(a) / sqrt(b).
5. Inverse operation: The square root function is the inverse of the square function. If f(x) = x^2, then the square root of f(x) is equal to x.

The square root function is widely used in various fields of mathematics, engineering, science, and finance. It plays an important role in solving equations, calculating distances, finding areas, and many other applications.

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