About This Chapter
ACT Compass Math: Roots & Radicals - Chapter Summary
You will become well-versed in the steps necessary to multiply radical expressions with two or more terms by studying the material in this chapter. Additional related topics that you could become comfortable with in time for the Compass Math test include:
- Dividing, multiplying and simplifying radical expressions
- Finding the cube root of a number
- Radical equations with two or more terms
- Calculating the square roots of quotients and estimating square roots
- Working with radicands and evaluating square roots of perfect squares
- Rationalizing denominators in radical expressions
- Simplifying square roots when not a perfect square
- Factoring radical expressions
Follow along with our professional instructors as they discuss these topics and more with the short and engaging video lessons. You can then easily backtrack in any video you review with the video tags.
Objectives of the ACT Compass Math: Roots & Radicals Chapter
The ACT Compass Math content areas require the ability to work with a variety of radical expressions and find roots. Information you see in this chapter is in the Compass Math placement test as well as the diagnostics tests used to help students get the right academic plan in order. The exam questions will be similar to the kinds of questions that you get practice with through this chapter's quizzes. The ACT Compass Math test includes questions that are in multiple-choice format.
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.
17. How to Find the Cube Root of a Number
After watching this video lesson, you will understand the process of finding the cube root of a number. Learn which numbers have an easy cube root to find and what the cube root means.
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Other chapters within the ACT Compass Math Test: Practice & Study Guide course
- Compass Math: Integers
- Compass Math: Decimals
- Compass Math: Fractions
- Compass Math: Exponents
- Compass Math: Percents
- Compass Math: Ratios, Rates & Proportions
- Compass Math: Median, Mean & Mode
- Compass Math: Algebraic Equations & Expressions
- Compass Math: Linear Equations
- Compass Math: Substituting Values
- Compass Math: Monomials & Polynomials
- Compass Math: Factoring Polynomials
- Compass Math: Matrices & Absolute Value
- Compass Math: Inequalities
- Compass Math: Complex Numbers
- Compass Math: Logarithms
- Compass Math: Basic Geometry
- Compass Math: Lines & Angles
- Compass Math: Polygons
- Compass Math: Triangles
- Compass Math: Quadrilaterals
- Compass Math: Circles
- Compass Math: Similar Figures
- Compass Math: Complex Figures
- Compass Math: Constructions
- Compass Math: Area, Circumference & Perimeter
- Compass Math: Mathematical Modeling
- Compass Math: Quadratics
- Compass Math: Quadratic Functions
- Compass Math: Trigonometric Functions
- Compass Math: Rational Functions
- Compass Math: Function Operations
- Compass Math: Trigonometric Identities
- Compass Math: Trigonometric Equations
- Compass Math: Trigonometric Applications
- Compass Math: Trigonometric Graphs
- Compass Math: Graph Symmetry
- Compass Math: Polar Coordinates & Parameterization