Lesson Plan-Multiplying and Dividing Radical Expressions

45 min.

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.

LEARNING STANDARDS:

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

VOCABULARY:

MATERIALS:

POD (5 min):

MINI-LESSON:

-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.

MINI-LESSON:

-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