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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
Interactive Graph: Square Root of x
The graph of the function
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 these related concepts: Inverse Variation, Quadratic Functions of the Form f(x) = a(xh)^2 + k, and Direct Variation
 e
 Appears in these related concepts: Derivatives of Exponential Functions, Natural Logarithms, and e
 exponent
 Appears in these related concepts: Logarithms of Products, Scientific Notation, and Logarithms of Quotients
 exponentiation
 Appears in these related concepts: Integer Exponents, Logarithmic Functions, and Simplifying Expressions of the Form log_a a^x and a(log_a x)
 expression
 Appears in these related concepts: Simplifying, Multiplying, and Dividing, Expressions and Sets of Numbers, and Bacterial Transformation
 function
 Appears in these related concepts: Inverse Functions, Solving Differential Equations, and Modal Mixture
 graph
 Appears in these related concepts: Graphing on Computers and Calculators, Reading Points on a Graph, and Graphing Functions
 imaginary
 Appears in these 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 these related concepts: Arithmetic Sequences, Sequences of Statements, and Summing Terms in an Arithmetic Sequence
 integer
 Appears in these related concepts: Exact Numbers, Scientific Notation, and Finding a Specific Term
 irrational number
 Appears in these related concepts: Zeroes of Polynomial Functions with Real Coefficients, Rational Coefficients, and Fractions
 operation
 Appears in these related concepts: Outsourcing, Merchant Wholesalers, and Designing the Operation
 parabola
 Appears in these related concepts: Quadratic Functions of the Form f(x) = ax^2 + bx + c, Where a is not Equal to 0, The Quadratic Formula, and Standard Equations of Hyperbolas
 point
 Appears in these related concepts: Circles, Relative Minima and Maxima, and Graphing Equations
 rational number
 Appears in these related concepts: Domain of a Rational Expression, Rational Exponents, and Real Numbers: Basic Operations
 real number
 Appears in these related concepts: Graphing the Normal Distribution, Intermediate Value Theorem, and The ComplexNumber System
 real numbers
 Appears in these related concepts: Finding Domains of Functions, Basics of Graphing Polynomial Functions, and Linear Inequalities
 relation
 Appears in these related concepts: Symmetry, Visualizing Domain and Range, and Functions and Their Notation
 series
 Appears in these related concepts: Taylor Polynomials, Charging a Battery: EMFs in Series and Parallel, and Resisitors in Series
 sign
 Appears in these related concepts: The Intermediate Value Theorem, Scientific Notation, and The Rule of Signs
 square
 Appears in these related concepts: Standard Form and Completing the Square, Special Factorizations and Binomials, and Radical Equations
 whole number
 Appears in these related concepts: Polynomials: Introduction, Addition, and Subtraction and Changing Logarithmic Bases
 zero
 Appears in these related concepts: The Discriminant, Finding Zeroes of Factored Polynomials, and Reducing Equations to a Quadratic
Sources
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Cite This Source
Source: Boundless. “Radical Functions.” Boundless Algebra. Boundless, 01 Jul. 2015. Retrieved 03 Jul. 2015 from https://www.boundless.com/algebra/textbooks/boundlessalgebratextbook/thebuildingblocksofalgebra1/radicalnotationandexponents14/radicalfunctions875517/