Understanding the Square Root Function | Explained with Examples and Properties

Square Root Function

The square root function is a mathematical function that returns the non-negative square root of a number

The square root function is a mathematical function that returns the non-negative square root of a number. It is denoted by the radical symbol (√) followed by the number inside the radical. The square root function is commonly written as f(x) = √x or y = √x.

The square root of a number x is defined as another number y, such that y multiplied by itself (y^2) equals x. In other words, if y is the square root of x, then y^2 = x.

For example:
√25 = 5, because 5 multiplied by itself (5^2) equals 25.
√9 = 3, because 3 multiplied by itself (3^2) equals 9.

It is important to note that the square root function returns the positive square root for positive numbers. For negative numbers, the square root does not exist within the real numbers and is considered undefined.

The square root function has several properties:
1. The square root of a positive number is always positive.
2. The square root of zero is zero.
3. The square root of a negative number is undefined within the real numbers (represented by the imaginary number, i, in complex numbers).

The square root function is used in various branches of mathematics and in real-life applications, such as calculating distances, finding sides of squares, and solving certain equations.

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