Lesson Plan-Multiplying and Dividing Radical Expressions

45 min.

Unit: Simplifying Radical Expressions

Class: 8th Grade Mathematics Lesson: Multiplying and Dividing Radical Expressions

PURPOSE: To multiply and divide expressions involving radical terms.

LEARNING OBJECTIVE: Students will be able to multiply and divide radical terms by applying strategies used previously while using the rules for radicals.


A.N.3 Perform the four arithmetic operations using like and unlike radical terms and express the result in simplest form


Radical Expression


POD (5 min):


-When you are asked to multiply and divide with radicals, you use the same strategies as you always have (i.e. distributive property, FOIL, etc), but you must also keep in mind the rules for multiplying with radicals

-Example: √3 (√6 + 7)

-Even though you are dealing with radicals, the same strategy applies for multiplying terms inside the parentheses—use the distributive property

-This simplifies to √3*√6 + √3*7

-Now you can use radical rules to simplify

-The first terms can simplify to √18, the second terms become 7√3

-You can still simplify √18 to √(9*2) = √9 *√2 = 3√2

-The expression becomes 3√2 + 7√3, which cannot be simplified any further so this is the final answer

SMALL: Simplify the following expressions:

1) √5 (√8 + 9) 2) (√6 – 3√21) (√6 + √21)

Answers: 1) 2√10 + 9√5 2) -57 – 6√14

WHOLE: Share out.


-When dividing by a radical, the rule is that a radical cannot remain in the denominator (it works like having 0 in the denominator—this can’t happen!)

-If you are dividing by a radical (it is in the denominator), multiply the numerator and denominator by the same exact radical to get rid of it

-Example: 2√3/√5

-Since there is √5 in the denominator, you must multiply both the numerator and denominator by √5

-This becomes 2√3*√5 / √5 *√5

-This simplifies to 2√15/√25 = 2√15/5

-Since there is no more radical in the denominator, the expression is simplified

SMALL: Simplify the following expressions:

1) 8√2/√7 2) 3√3/√12

Answers: 1) 8√14/7 2) 3/2

WHOLE: Share out.

Use study island to administer individual practice and assessment on the topic of radicals

REFLECTION (10 min): How do you multiply and divide with radicals? What do you have to be aware of?

HOMEWORK: Try to earn blue ribbon in the topic of radicals on study island

*Use the results from study island to identify students that need the extra support to meet the standards of radicals.

Since some questions are more advanced than necessary, use the results to also identify students prepared to discuss and investigate the “above-standard” material associated with radical expressions.