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Square Roots and Radical Expressions
Solving Radical Equations
Simplifying Radical Expressions
Irrational Numbers in General and Square Roots in Particular
Roots of Polynomials
Simplifying Radical Expressions
Exponents and Radicals
Products and Quotients Involving Radicals
Roots of Quadratic Equations
Radical Expressions
Radicals and Rational Exponents
Find Square Roots and Compare Real Numbers
Radicals
Radicals and Rational Exponents
Theorems on the Roots of Polynomial Equations
SYNTHETIC DIVISION AND BOUNDS ON ROOTS
Simplifying Radical Expressions
Exponents and Radicals
Properties of Exponents and Square Roots
Solving Radical Equations
Rational Exponents and Radicals,Rationalizing Denominators
Rational Exponents and Radicals,Rationalizing Denominators
Quadratic Roots
Exponents and Roots
Multiplying Radical Expressions
Exponents and Radicals
Solving Radical Equations
Solving Quadratic Equations by Factoring and Extracting Roots
Newton's Method for Finding Roots
Roots of Quadratic Equations Studio
Roots, Radicals, and Root Functions
Review division factoring and Root Finding
Radicals
Simplifying Radical Expressions
Multiplying and Simplifying Radical Expressions
LIKE RADICALS
Multiplication and Division of Radicals
Radical Equations
BOUNDING ROOTS OF POLYNOMIALS
   
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Radicals and Rational Exponents

Definition of the Principal Square
Root

• If a is nonnegative real number, the
nonnegative number b such that
denoted by ,is the principle square
root
of a

Square Roots of Perfect Square

The Product Rule for Square Roots

• If a and b represent nonnegative real
number, then
 

and

• The square root of product is the product
of the square roots

Text Example

• Simple :

solution :

The Quotient Rule for Square Roots

• If a and b does represent nonnegative real
numbers and b does no equal 0, then

and 

• The square root of quotient  is the
quotient of the square roots

Text Example

• Simple :

solution :

Example

• Perform the indicated operation:

solution :

• Perform the indicated operation:

solution :

Definition of the Principal nth Root
of a Real Number

means that

• If n ,the index , is even , then a is
nonnegative (a≥0)and b is also
nonnegative (b≥0).If n is odd ,a and b
can be any real numbers.
 

Finding the nth Roots of Perfect
th Powers

If n is odd ,
If n is even

The Product and Quotient Rules
for nth Roots

• For all real numbers ,where the indicated
roots represent real numbers,

and 

 Definition of Rational Exponents

Furthermore

Example

• Simple :

solution:

Definition of Rational Exponents

•The exponents m/n consists of two parts :the
denominator n is the root and the numerator
m is  the exponent. Furthermore .

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