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Radical Functions
An expression with roots is called a radical function, there are many kinds of roots, square root and cube root being the most common.
Learning Objective

Discover how to graph radical functions by examining the domain of the function
Key Points

Roots are the inverse operation for exponents. If
$\sqrt [ n ]{ x } = r$ then${r}^{n}=x$ . 
If the square root of a number is taken, the result is a number which when squared gives the first number.

The cube root is the number which, when cubed, or multiplied by itself and then multiplied by itself again, gives back the original number.

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.
Terms

radical
A root (of a number or quantity).

root
the number which,when plugged into the equation, will produce a zero.
Full Text
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.
For instance
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
Square root
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:
In the series of real numbers
Such examples of square roots can be seen in .
Cube roots
Roots do not have to be square.
The cube root of a number (
Other roots
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 90degrees clockwise.
For example, the graph of
Irrational numbers
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 nonsquare number as
Key Term Reference
 constant
 Appears in this related concepts: Inverse Variation, Combined Variation, and Quadratic Functions of the Form f(x) = a(xh)^2 + k
 e
 Appears in this related concepts: Derivatives of Exponential Functions, Derivatives of Logarithmic Functions, and Natural Logarithms
 exponent
 Appears in this related concepts: Logarithmic Functions, Scientific Notation, and Logarithms of Quotients
 exponentiation
 Appears in this related concepts: Integer Exponents, Logarithmic Functions, and Simplifying Expressions of the Form log_a a^x and a(log_a x)
 expression
 Appears in this related concepts: Simplifying, Multiplying, and Dividing, Compound Inequalities, and Bacterial Transformation
 function
 Appears in this related concepts: Solving Differential Equations, Four Ways to Represent a Function, and Average Value of a Function
 graph
 Appears in this related concepts: Graphing on Computers and Calculators, Graphing Equations, and Equations and Their Solutions
 imaginary
 Appears in this related concepts: Addition, Subtraction, and Multiplication, The Fundamental Theorem of Algebra, and Complex Conjugates and Division
 imaginary number
 Appears in this related concept: Complex Numbers
 infinite
 Appears in this related concepts: Arithmetic Sequences, Sequences of Statements, and Summing Terms in an Arithmetic Sequence
 integer
 Appears in this related concepts: Scientific Notation, Total Number of Subsets, and Finding a Specific Term
 irrational number
 Appears in this related concepts: Zeroes of Polynomial Functions with Real Coefficients, Rational Coefficients, and Fractions
 operation
 Appears in this related concepts: Designing the Operation, The Importance of Clarity in Professional Settings, and Converting between Exponential and Logarithmic Equations
 parabola
 Appears in this related concepts: Standard Form and Completing the Square, Quadratic Functions of the Form f(x) = ax^2 + bx + c, Where a is not Equal to 0, and Quadratic Equations and Quadratic Functions
 point
 Appears in this related concepts: Circles, Relative Minima and Maxima, and Introduction: Polynomial and Rational Functions and Models
 rational number
 Appears in this related concepts: Domain of a Rational Expression, Rational Exponents, and Real Numbers: Basic Operations
 real number
 Appears in this related concepts: Graphing the Normal Distribution, Solving Problems with Inequalities, and The ComplexNumber System
 real numbers
 Appears in this related concepts: Piecewise Functions, Linear Inequalities, and Factoring Trinomials of the Form ax^2 + bx + c; Perfect Squares
 relation
 Appears in this related concepts: Symmetry, Visualizing Domain and Range, and Functions and Their Notation
 series
 Appears in this related concepts: Taylor Polynomials, Charging a Battery: EMFs in Series and Parallel, and Resisitors in Series
 sign
 Appears in this related concepts: The Intermediate Value Theorem, The Rule of Signs, and Polynomial Inequalities
 square
 Appears in this related concepts: Special Factorizations and Binomials, Radical Equations, and Matrix Multiplication
 whole number
 Appears in this related concepts: Basics of Graphing Polynomial Functions, Polynomials: Introduction, Addition, and Subtraction, and Changing Logarithmic Bases
 zero
 Appears in this related concepts: Zeroes of Linear Functions, Rational Inequalities, and Finding Zeroes of Factored Polynomials
Sources
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Cite This Source
Source: Boundless. “Radical Functions.” Boundless Algebra. Boundless, 03 Jul. 2014. Retrieved 20 May. 2015 from https://www.boundless.com/algebra/textbooks/boundlessalgebratextbook/thebuildingblocksofalgebra1/radicalnotationandexponents14/radicalfunctions875517/