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Exponents and Radicals
Division of Radicals
Exponents and Radicals
RADICALS & RATIONAL EXPONENTS
Radicals and Rational Exponents
Radical Equations
Solving Radical Equations
Roots and Radicals
RADICAL EQUATION
Simplifying Radical Expressions
Radical Expressions
Solving Radical Equations
Solving Radical Equations
Exponents and Radicals
Exponents and Radicals
Roots;Rational Exponents;Radical Equations
Solving and graphing radical equations
Solving Radical Equations
Radicals and Rational Exponents
exponential_and_radical_properties
Roots, Radicals, and Root Functions
Multiplication of Radicals
Solving Radical Equations
Radical Expressions and Equations
SOLVING RADICAL EQUATIONS
Equations Containing Radicals and Complex Numbers
Square Roots and Radicals
Solving Radical Equations in One Variable Algebraically
Polynomials and Radicals
Roots,Radicals,and Fractional Exponents
Adding, Subtracting, and Multiplying Radical Expressions
Square Formula and Powers with Radicals
Simplifying Radicals
Exponents and Radicals Practice
Solving Radical Equations
Solving Radical Equations
Solving Radical Equations
Lecture-Radical Expressions
Radical Functions
   
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Radicals and Rational Exponents

Definition of the Principal Square
Root

• If a is a nonnegative real number, the
nonnegative number b such that b2 = a,
denoted by is the principal square
root
of a.

Square Roots of Perfect Squares

The Product Rule for Square Roots

• If a and b represent nonnegative real
number, then

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

Text Example

• Simplify

Solution:

The Quotient Rule for Square Roots

• If a and b represent nonnegative real
numbers and b does not equal 0, then

and

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

Text Example

• Simplify:

Solution:

Example

• Perform the indicated operation:

Solution:

Example

• 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
nth Powers

If n is odd,
If n is even an

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

• Simplify

Solution:

Definition of Rational Exponents

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

Radicals and
Rational Exponents
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