1. Multiplying and Dividing Radical Expressions.
Binomial Radical Expressions.
What you’ll learn
To multiply and divide radical expressions.
To add and subtract radical expressions.
Vocabulary
Simplest form of a radical, rationalize
the denominator, like radicals

2. Take a note:
You can simplify the product of powers that have
the same exponent. Similarly, you can simplify the
product of radicals that have the same index You can.
You can simplify a radical expression when the exponent
of one factor of the radicand is a multiple of the
radical’s index.
Example:

3. Problem 1: Multiplying Radical Expressions.
Can you simplify the product of the radical expressions?
Explain.
Your turn
Can you simplify the product of the radical expressions?
Explain.
Answer:

4. Problem 2: Simplifying a radical Expression
If the radicand has a perfect nth power
among its factors, you can reduce the
radical.. If you reduce a radical as much
as possible, the radical is in the simplest form
Problem 2: Simplifying a radical Expression
Your turn
Answer:

5. Problem 3:Simplifiying a Product
Answer
Your turn
Answers:

6. Problem 4: Dividing Radical Expressions
You can extend the property for multiplying radical expressions.
If the indexes are the same , you can write a quotient of roots
as a root of quotient.
Problem 4: Dividing Radical Expressions
What is the simplest form of the quotient?

7. Your turn Answer: Problem 5: Rationalizing the Denominator
Note: Another way to simplify an expression is to rationalize the denominator . You rewrite the expression so that there are no radicals in any denominator and no denominator in any radical. Do the factorization of the denominator and choose what to multiply by. What do you need to make each factor of the radicand in the denominator a perfect cube.
Problem 5: Rationalizing the Denominator
What the denominator is missing
to get out of the radical?

8. Your turn
Answer:
Take a note: Like radicals are radical expressions that have the same index and radicand. You can combine like radicals using properties of real numbers. When adding or subtracting
remember to simplify first.
When multiplying binomial radicals expressions use FOIL

9. What is the simplified form of each expression?
Problem 6: Adding and Subtracting Radical Expressions
What is the simplified form of each expression?
The radicands are different.
You cannot combine the expressions
The indexes are different.
You cannot combine the expressions
Your turn
What is the simplified form of each expression?
The indexes are different.
You cannot combine the
expressions

10. Your turn again: Using radical expression
1.)This tile design is made of congruent right triangles with base 1 ft and height 2 ft. Find the perimeter of the tile to the nearest tenth of a foot.
Answer: Hint use P.T. to find c
2.) What is the simplest form of the expression?
(remember to simplified before adding or subtracting)
Answer:

11. Problem 7: Multiplying Binomial Radical Expressions
What is the product of each radical expression?
Multiplying
conjugates
Your turn: What is the product of each radical expression
Answers:

12. Problem 8: Rationalizing the denominator
How can you write the expression with a rationalized
denominator?
Take a note: Conjugate are
expressions that
only differ in the signs of
the second term
Your turn: How can you write the expression with a
rationalized denominator
Answer

13. Classwork odd Homework even
TB pgs exercises 10-68
TB pgs exercises 10-64