About This Chapter
ACT Math: Radicals - Chapter Summary
This chapter can help you prepare for intermediate algebra questions found on the math section of the ACT. Use the following lessons on square roots and radical expressions to learn how to:
- Find, estimate and simplify square roots
- Evaluate square roots of perfect squares
- Factor, multiply and divide radical expressions
- Rationalize denominators in radical expressions
- Add and subtract using radical notation
- Multiply radical expressions with two or more terms
- Solve radical equations with two radical terms
Radical expressions might look complicated, but our experienced instructors provide you with plenty of tips for simplifying and factoring these equations so you can cut them down to size. Lesson content is available in the form of short videos and matching transcripts that allow you to work at your own pace. There are also multiple-choice quizzes you can take at any point during your studies to get an idea of how exam questions are formatted and review each lesson's main ideas.
ACT Math: Radicals - Chapter Objectives
The ACT is a standardized test used by college and university admissions departments to gauge your ability to succeed in a college classroom. It includes English, reading and science portions in addition to a writing section required by some schools.
The math portion of the ACT gives you one hour to complete 60 multiple-choice questions on algebra, geometry and trigonometry. You can use lessons included in this chapter to study for the 15% of test questions assessing your understanding of radical expressions and other intermediate algebra topics.
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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