Mastering The Square Root Function: Applications And Properties Explained

Square Root Function

f(x) = √x

The square root function is a mathematical function that takes a non-negative real number as input and returns its non-negative square root as output. In other words, if we have a number x, the square root function will return the non-negative number y such that y^2 = x.

The symbol for the square root function is √, and it is typically written before the number that we want to take the square root of. For example, √9 = 3, since 3 is the non-negative number that, when squared, gives us 9.

The square root function is often used in algebra and geometry, since it can help us solve equations involving square roots as well as find the lengths of sides of right triangles. It is also used in calculus and other advanced areas of mathematics.

Some important properties of the square root function include:

– The square root of a negative number is not a real number, since the square of any real number is always non-negative. However, we can define a complex version of the square root function for negative numbers.
– The square root function is one-to-one, which means that no two distinct inputs will give us the same output.
– The graph of the square root function is a curve that starts at the origin and increases without bound as its input (the radicand) increases.

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