Algebra Tutorials! Home 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

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: Perfect Square ▪ Simplify: Perfect Square ▪ Simplify: Square roots
undo squares ▪ 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:  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