About This Chapter
Algebra II: Roots and Radical Expressions Review - Chapter Summary and Learning Objectives
This chapter can show you how to find, estimate and simplify square roots. You'll also practice factoring, multiplying and dividing radical expressions. Later lessons look at how to solve equations with multiple radical terms. Upon finishing this chapter, you should have a firm understanding of the following concepts:
- Square roots
- Radicands and radical expressions
- Perfect squares
- Radical equations
|How to Find the Square Root of a Number||Understand how to calculate the square root of any given number.|
|Estimating Square Roots||Know how to best estimate the square root of a number.|
|Simplifying Square Roots When Not a Perfect Square||Learn how to simplify square roots that are not a perfect square.|
|Simplifying Expressions Containing Square Roots||Simplify expressions that contain square roots in their equation.|
|Radicands and Radical Expressions||Recognize radicands and radical expressions and identify whether a radical expression represents a real number.|
|Evaluating Square Roots of Perfect Squares||Simplify a radical expression with a perfect square radicand.|
|Factoring Radical Expressions||Be able to factor and multiply radical expressions, detailing the product rule for radicals.|
|Simplifying Square Roots of Powers in Radical Expressions||Demonstrate how to solve radical expressions where the radicands are powers.|
|Multiplying Then Simplifying Radical Expressions||Understand how to multiply radical expressions, and when possible, simplify to solve the problem.|
|Dividing Radical Expressions||Successfully divide radical expressions.|
|Simplifying Square Roots of Quotients||Show how to simplify the square roots of quotients, providing examples.|
|Rationalizing Denominators in Radical Expressions||Explain how to rationalize the denominator of a radical expression.|
|Addition and Subtraction Using Radical Notation||Use the distributive laws to add and subtract with radical notation.|
|Multiplying Radical Expressions with Two or More Terms||Multiply expressions involving radicals with two or more terms.|
|Solving Radical Equations: Steps and Examples||Use the principle of squaring once to solve radical equations with one or two radical terms isolated.|
|Solving Radical Equations with Two Radical Terms||Employ the principle of squaring twice to solve radical equations with two radical terms.|
1. How to Find the Square Root of a Number
What is a square root? In this lesson, we'll learn what a square root is and how to find it. We'll review a variety of examples in order to master the concept.
2. Estimating Square Roots
Inverse operations are mathematical operations that undo each other. The square root is the inverse of the squared (or multiplying a number by itself) operation. There is an easy method for estimating the square root of a number, which you will learn in this lesson.
3. Simplifying Square Roots When not a Perfect Square
Numbers that are imperfect squares are those that, when evaluated, do not give solutions that are integers. The proper mathematical way to simplify these imperfect squares is discussed in this lesson.
4. Simplifying Expressions Containing Square Roots
In order to write radical expressions correctly, they have to be written in their simplest form. This lesson will show you how to simplify expressions containing numbers and variables inside a square root.
5. Radicands and Radical Expressions
It's easy to see that funky radical symbol and panic just a little bit. There are so many rules that go along with it, it's hard to keep up with them all. This lesson will help by describing what you should do when you are faced with a square root.
6. Evaluating Square Roots of Perfect Squares
Squares and square roots are inverse, or opposite, operations involving radicals. Learn how to determine the square root of perfect squares in this lesson.
7. Factoring Radical Expressions
Watch this video lesson to learn how to apply the product rule to your radical expressions. Learn how this product rule actually helps you to simplify your radicals as well.
8. Simplifying Square Roots of Powers in Radical Expressions
Simplifying radical expressions that contain powers can be tricky. There are a few simple rules that will help you perform these simplifications with ease. This lesson will teach you how.
9. Multiplying then Simplifying Radical Expressions
Multiplying 2 or more radical expressions uses the same principles as multiplying polynomials, with a few extra rules for dealing with the radicals. This lesson will teach you how to multiply and then simplify radical expressions.
10. Dividing Radical Expressions
When dividing radical expressions, we use the quotient rule. This lesson will describe the quotient rule and how to use it to solve these radical expressions.
11. Simplify Square Roots of Quotients
The quotient rule can be used to simplify square roots of quotients. This lesson will define the quotient rule and show you how it is used to simplify square roots.
12. Rationalizing Denominators in Radical Expressions
Radical expressions containing denominators are not simplified completely unless the denominator is free of radical symbols. This lesson will teach you how to remove a radical from the denominator of a fraction through a process called rationalizing the denominator.
13. Addition and Subtraction Using Radical Notation
There are specific rules governing adding and subtracting radical expressions. This lesson will describe these rules and give examples of how they are used.
14. Multiplying Radical Expressions with Two or More Terms
Multiplying radical expressions with more than two terms can be confusing. This lesson will take some of the confusion away by giving clear steps for multiplying these expressions. It will also provide some examples to help solidify the steps.
15. Solving Radical Equations: Steps and Examples
Solving radical equations is not any more difficult than solving other algebraic equations. This lesson will show you how to solve equations containing a square root and give some real-world examples.
16. Solving Radical Equations with Two Radical Terms
Solving equations with two radical terms takes some patience and care, but it really is not difficult. This lesson will show you the steps to solve these more complicated equations plus give you some examples to follow.
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Other chapters within the Algebra II: High School course
- Algebra II: Real Numbers
- Algebra II: Complex and Imaginary Numbers Review
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Properties of Functions Review
- Algebra II: Linear Equations Review
- Algebra II: Systems of Linear Equations
- Algebra II: Inequalities Review
- Algebra II: Absolute Value Review
- Algebra II: Graphing and Factoring Quadratic Equations Review
- Algebra II: Quadratic Equations
- Algebra II: Factoring
- Algebra II: Polynomials
- Algebra II: Rational Expressions
- Algebra II: Graphing and Functions
- Algebra II: Conic Sections
- Algebra II: Exponential and Logarithmic Functions
- Algebra II: Sequences & Series
- Algebra II: Combinatorics
- Algebra II: Calculations, Ratios, Percent & Proportions Review
- Algebra II: Statistics
- Algebra II: Trigonometry
- Teacher Resources for High School Algebra II