The sqrt function allows to calculate the square root of a number in exact form.

Square root function

By definition, the square root of a real number x, is a number which squared is equal to x.

Calculation of the square root

The square root calculator allows through the sqrt function to calculate online the square root.

For example, to calculate the square root of 9 which notes `sqrt(9)`, enter sqrt(`9`), after calculating the result 3 is returned.

For example, to calculate the square root of 99 which notes `sqrt(9)` enter sqrt(`99`), after calculating the result `3*sqrt(11)` is returned.

Note that the result of the square root calculation is returned in its exact form.

Derivative of square root

The derivative of the square root is equal to `1/(2*sqrt(x))`.

Antiderivative of square root

The antiderivative of the square root is equal to `2/3*(x)^(3/2)=2/3*(sqrt(x))^3`.

Limit of square root

The limit of the square root exist at `+oo` (plus infinity):
• The square root function has a limit in `+oo` which is `+oo`.
`lim_(x->+oo)sqrt(x)=+oo`

Syntax :

sqrt(x), x is a number.

Examples :

sqrt(`4`), returns 2

Derivative square root :

To differentiate function square root online, it is possible to use the derivative calculator which allows the calculation of the derivative of the square root function

The derivative of sqrt(x) is derivative(`sqrt(x)`)=`1/(2*sqrt(x))`

Antiderivative square root :

Antiderivative calculator allows to calculate an antiderivative of square root function.

An antiderivative of sqrt(x) is antiderivative(`sqrt(x)`)=`2/3*(x)^(3/2)`

Limit square root :

The limit calculator allows the calculation of limits of the square root function.

The limit of sqrt(x) is limit(`sqrt(x)`)

Graphic square root :

The graphing calculator is able to plot square root function in its definition interval.

• Simplifying surds calculator : simplify_surd. Online surds calculator that allows you to make calculations in exact form with square roots: sum, product, difference, ratio.
• Cube root : cube_root. The cube_root function calculates online the cube root of a number.
• Square root : sqrt. The sqrt function allows to calculate the square root of a number in exact form.