Lesson 3
1. Lesson 3
1.5. Explore
Module 5: Radicals
Explore
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As you saw in the Discover section, adding and subtracting radicals works the same as adding and subtracting like terms. In the case of radicals, the radicands are considered the like terms. Just as you can’t always simplify a variable expression all the way down to one term, you can’t always simplify a radical expression down to one term. We have all heard the expression “you can’t add apples and oranges.” In order to add or subtract radical terms, they have to have the same radicand and index.
like terms: terms that have the same set of variable bases and corresponding exponents
For example, 6x and 13x are like terms with a variable base of x to the exponent 1. They are like terms since they have the common variable factor of x.
Did You Know?
Square roots and cube roots can be written with fractional exponents. For example,
For that reason, radical expressions can be treated just like other variables with exponents and polynomials. The rules that apply to monomial and binomial expressions also apply to radicals when adding, subtracting, multiplying, and dividing. In the same way that you can’t combine by addition
4n4 + 2n3 because they are not like terms, you can’t add 
The same distributive property and multiplication properties apply to radical expressions as apply to other expressions.
Selena and Josh are working together on their homework, and the assignment is to simplify some radical expressions that require adding and subtracting. They use different methods to simplify the expressions. Look at Selena’s and Josh’s Solutions to decide which method you would prefer to use when simplifying radicals.
Read “Example 3: Simplifying radical expressions” on pages 186 and 187 of your textbook. As you read, look closely at the strategies Vanessa uses to simplify the radical expressions. What is the first step that she used in both questions?
Self-Check 1
- For each of the following questions, simplify by adding or subtracting.
- Simplify the following radicals, and then combine like terms.
- Simplify radicals and combine like terms.
Answers
- Complete “Practising” question 10 on page 189 of your textbook. Answer
If you haven’t done so already, now would be a good time to update your Glossary Terms document. Remember to save your updated document to your course folder.
The term to be added for this lesson is
- like terms