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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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Solving Radical Equations

8.1 Definitions and Roots

▪ Need To Know
▪ How to find the root of a number
▪ Categorizing roots
▪ How to find the root of an expression
▪ How to solve application problems
involving roots

Idea of Square Roots

In mathematics, once we learn an operation,
we also learn the reverse of that operation.

For real numbers x and y,
If y = x2 then x = ___

Don’t Forget
Radicand
Radical Sign
Radical

Definitions and Roots

Definition – If x is any positive real number, then
is the square root of x and
is the square root of x.

Examples:
Name the two square roots of 81.

Find the root of

Simplify

Evaluate

Recall Number Sets

▪ Rational Numbers
are the numbers of
the form a/b where
b is not zero.

▪ Rational Numbers is
the set of all fractions

Recall Number Sets


▪ Irrational Numbers
are the numbers
that can not be
written as fractions

▪ Real Numbers are
the collection of all
Rational and
Irrational Numbers.

Categorize Roots

Square Roots & Absolute Value

Consider and

Both come out positive.

Recall: |-7| = 7 and |7| = 7.

For all real numbers A, ___________________

Examples:

Application

The speed of sound in feet per second, V, traveling
through air with a temperature of t is given by the
formula below. Find the speed of sound when the
temperature is 5° C.

8.1 Conclusion

▪ The square root is the number that
“undoes” the square.
▪ Square roots can be positive or negative.
▪ The square root of zero is zero.
▪ The square root of a negative number is
not a Real Number
▪ A square root results in a
Rational, Irrational or Non-Real Number

8.2 Multiply and Simplify Radicals

▪ Need To Know

▪ Multiplying of radicals
▪ Simplifying radical expressions
1. With numbers
2. With variables

Multiplication Property of Radicals

▪ If A and B are real numbers (> 0), then
______________________________

Simplify Radical Expressions

 

▪ Simplify:


 

Perfect
Square


 

Simplify Radical Expressions

▪ Simplify:

Perfect
Square

Simplify Radical Expressions

▪ Simplify:

Square roots
undo squares

Practice Simplifying Radicals
▪ Simplify:

end

8.3 Properties of Radicals

▪ Need To Know
▪ Quotient Rule for Square Roots
▪ Simplifying radical expressions
1. With Fractions
2. By Rationalizing the Denominator

Quotient Rule for Square Roots
▪ If A and B are real numbers (B ≠ 0),
then
__________________________________

Simplify Radical Expressions
▪ Simplify:

The Idea of a Simplified Radical

Which fraction is the simplest?

Rationalizing Denominators

▪ Goal: Change the fraction to make the
denominator come out “nice”.

Guidelines for Simplification

1. Remove ____________________________
2. Remove ____________________________
3. Remove ____________________________

▪ Examples:

Guidelines for Simplification

1. Remove fractions from radicals
2. Remove perfects for radicals
3. Remove radicals from denominators

▪ Examples:

end

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