Learning Resources
Outcomes
By the end of this lesson you will be able to answer questions like the ones in the pre-test below.
First answer the questions on the pre-test below in your Math 3103 binder. Then refer to the pages of the lesson that contain instruction on the questions for which you get an incorrect answer or for which you would like some further explanation.
Alternately, you can proceed directly to the first page of the lesson without doing the pre-test. To do this simply click on the Lesson button above. You can then return to this pre-test and use it as a worksheet.
Pre-test
Find each of the following roots. Do not use a calculator.
1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 
19. 
20. 
By the end of this section you should be able to:
- Define the expression
and write these expressions in simplest form. - Multiply and divide expressions containing radicals.
- Add and subtract expression containing radicals.
- Rationalize the denominator of a fraction.
Introduction
This section contains five lessons as follows:
Lesson 01 Definition of Radicals
In this lesson you will learn the definition of . You will then apply this definition to evaluate and simplify expressions which contain it.
Lesson 02 Multiplying and Dividing Radicals
In this lesson you will multiply and divide radicals. For example you will work with expressions like 
and see how it is equal to 
. Also you will see how an expression like 
can be written as 
.
Lesson 03 Simplifying Radicals
In this lesson you will learn to simplify radicals. For example you will work with expressions like 
and see how it is equal to 
.
Lesson 04 Adding and Subtracting Radicals
In this lesson you will add and subtract radicals. You will learn the definition of "like radicals" and see how only like radicals can be added. For example you will see how expressions like 
can be written as 
(note that it is NOT equal to 
).
Lesson 05 Rationalizing the Denominator
In this lesson you will learn how to make the denominator of a fraction which contains a radical, which is an irrational number, a rational number. For example you will learn how an expression like 
can be written as 
.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- The definition of the square root of a number.
- How to express a number using exponents.