A function

*f*from \(\mathbb{R}\) to \(\mathbb{R}\) in which the variable appears in the radicand of a radical of order 2.The square root function is sometimes called a

The basic form of the rule of a square root function is \(f(x) = \sqrt{x} \).

The standard form of the rule of the square root function is \(f(x) = a\sqrt{b(x − h)} + k \) where

*radical function of order 2*or a*root function of order 2*.The basic form of the rule of a square root function is \(f(x) = \sqrt{x} \).

The standard form of the rule of the square root function is \(f(x) = a\sqrt{b(x − h)} + k \) where

*a*is not equal to zero and*b*> 0.The square root function is a particular case of an *n*th root function.

### Example

Consider the function *f*(*x*)=\(2\sqrt{0.5\left ( x – 3 \right )} + \left ( -1 \right )\)

### Educational notes

- The square root function, also called a
*radical function of order 2*, is derived from the reciprocal relation of the second-degree polynomial function. Although this reciprocal relation is not a function, two square root functions may be derived from it : one positive and one negative.

- For example, if
*f*is a polynomial function defined by the relation*y*= 0.5*x*\(^{2}\) + 20, then the reciprocal relationship is obtained by interchanging the two variables:*x*= 0.5*y*\(^{2}\) + 20. By isolating*y*, we obtain :*y*= ± \( \sqrt{2x – 20} \).