About This Chapter
How it works:
- Identify the lessons in the Glencoe Algebra 1 Radical Expressions and Triangles chapter with which you need help.
- Find the corresponding video lessons within this companion course chapter.
- Watch fun videos that cover the radical expressions and triangles topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.
Students will learn:
- Radicals, radicands and radical expressions
- Simplification of expressions containing square roots
- Multiplication and simplification of radical expressions
- Division of radical expressions
- Solutions of radical equations with two radical terms
- The Pythagorean Theorem and its applications
- Identification and applications of similar triangles
- Trigonometric ratios
- Angle of elevation and angle of depression
Glencoe is a registered trademark of McGraw-Hill Education, which is not affiliated with Study.com.
1. 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.
2. 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.
3. How to Rationalize the Denominator with a Radical Expression
Watch this video lesson to learn what you can do to simplify your expression when you have a radical in the denominator. Learn what the single step solution to your problem is.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
9. Pythagorean Theorem: Definition & Example
Learn what the Pythagorean Theorem says about a right triangle and the relationships of its three sides to each other by watching this video lesson. Also learn how you can use this to your advantage when solving problems.
10. Understanding Numbers That Are Pythagorean Triples
In this video lesson, you will learn about numbers that form Pythagorean Triples. Learn why these are special numbers and what they have to do with triangles.
11. The Pythagorean Theorem: Practice and Application
The Pythagorean theorem is one of the most famous geometric theorems. Written by the Greek mathematician Pythagoras, this theorem makes it possible to find a missing side length of a right triangle. Learn more about the famous theorem here and test your understanding with a quiz.
12. Finding Distance with the Pythagorean Theorem
How much faster is it to cut the corners in a race around the block? In this lesson, review the Pythagorean Theorem, and figure out how to solve without a right triangle.
13. How to Use The Distance Formula
You can't always rely on your smartphone to tell you how far you need to travel to get from point A to point B. The distance formula will tell you the distance between any two points on a graph. In this lesson, you'll learn where it comes from and how to use it!
14. How to Identify Similar Triangles
Similar triangles have the same characteristics as similar figures but can be identified much more easily. Learn the shortcuts for identifying similar triangles here and test your ability with a quiz.
15. Applications of Similar Triangles
Similar triangles are used to solve problems in everyday situations. Learn how to solve with similar triangles here, and then test your understanding with a quiz.
16. Trigonometric Ratios and Similarity
Where do terms like sine, cosine and tangent come from? In this lesson, we'll learn about how similarity with right triangles leads to trigonometric ratios.
17. Practice Finding the Trigonometric Ratios
So you know what sine, cosine and tangent are. Great! But how do you use them? Find out how in this lesson as we find missing sides and angles using trigonometric ratios.
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Other chapters within the Glencoe Algebra 1: Online Textbook Help course
- Glencoe Algebra 1 Chapter 1: The Language of Algebra
- Glencoe Algebra 1 Chapter 2: Real Numbers
- Glencoe Algebra 1 Chapter 3: Solving Linear Equations
- Glencoe Algebra 1 Chapter 4: Graphing Relations and Functions
- Glencoe Algebra 1 Chapter 5: Analyzing Linear Equations
- Glencoe Algebra 1 Chapter 6: Solving Linear Inequalities
- Glencoe Algebra 1 Chapter 7: Solving Systems of Linear Equations and Inequalities
- Glencoe Algebra 1 Chapter 8: Polynomials
- Glencoe Algebra 1 Chapter 9: Factoring
- Glencoe Algebra 1 Chapter 10: Quadratic and Exponential Functions
- Glencoe Algebra 1 Chapter 12: Rational Expressions and Equations
- Glencoe Algebra 1 Chapter 13: Statistics
- Glencoe Algebra 1 Chapter 14: Probability