Roots are the inverse operation for exponents.
An expression with roots is called a radical expression.
It's easy, although perhaps tedious, to compute exponents given a root.
If fourth root of 2401 is 7, and the square root of 2401 is 49, then what is the third root of 2401?
Finding the value for a particular root is difficult. This is because exponentiation is a different kind of function than addition, subtraction, multiplication, and division. When graphing functions, expressions that use exponentiation use curves instead of lines. Using algebra will show that not all of these expressions are functions and that knowing when an expression is a relation or a function allows certain types of assumptions to be made. These assumptions can be used to build mental models for topics that would otherwise be impossible to understand.
For now, deal with roots by turning them back into exponents. If a root is defined as the nth root of X, it is represented as
If the square root of a number is taken, the result is a number which when squared gives the first number.
This can be written symbolically as:
Such examples of square roots can be seen in .
Roots do not have to be square.
The cube root of a number (
There are an infinite number of possible roots all in the form of
Graphs of Radical Functions
Since roots are simply the inverse of exponents, graphing roots can be seen as just graphing exponents with the axes reversed.
The shape of the radical graph will resemble the shape of the related exponent graph it were rotated 90-degrees clockwise.
For example, the graph of
If a root of a whole number is squared root, which is not itself the square of a rational number, the answer will have an infinite number of decimal places.
Such a number is described as irrational and is defined as a number which cannot be written as a rational number:
The result of taking the square root is written with the approximately equal sign because the result is an irrational value which cannot be written in decimal notation exactly.
Writing the square root of 3 or any other non-square number as