Chapter 5 Section 6
Objectives:
•To simplify radical expressions.
•To add, subtract, multiply and divide
radical expressions
Warm-up: Type 1 writing
3 lines or more – 2 minutes
Describe the steps involved in finding the 6th
root of a number on your calculator. How
could you check to make sure that your
answer is correct?
30 seconds
Finish your thought.
Warm-up: Type 1 writing
3 lines or more – 2 minutes
Describe the steps involved in finding the 6th
root of a number on your calculator. How
could you check to make sure that your
answer is correct?
Times up!
Put your pencils
down.
Product Property of Radicals
If n is even
and a and b are both nonnegative, then
ab  a  b
If n is odd, then
n
n
n
n
ab  a  b
n
n
Example 1 Square Root of a Product
Example 2 Simplify Quotients
Example 3 Multiply Radicals
Example 4 Add and Subtract Radicals
Example 5 Multiply Radicals
Example 6 Use a Conjugate to Rationalize
a Denominator
Simplify
Factor into squares
where possible.
Product Property
of Radicals
Answer:
Simplify.
Simplify
Answer:
Quotient Property of Radicals
For b  0
n
n
a
a
 n
b
b
Note:
You can not leave a radical in the denominator!
Simplify
Quotient Property
Factor into squares.
Product Property
Rationalize the denominator.
Answer:
Simplify
Quotient Property
Rationalize the denominator.
Product Property
Multiply.
Answer:
Simplify each expression.
a.
Answer:
b.
Answer:
Simplifying Radical Expressions
A radical expression is in simplified form
when:
The index n is as small as possible.
Simplifying Radical Expressions
A radical expression is in simplified form
when:
The radicand contains no factors
(other than 1) that are nth powers of an
integer or polynomial.
Simplifying Radical Expressions
A radical expression is in simplified form
when:
The radicand contains no fractions.
Simplifying Radical Expressions
A radical expression is in simplified form
when:
No radicals appear in the denominator
(This is what is meant by rationalizing the
denominator)
Simplify
Product Property
of Radicals
Factor into cubes.
Product Property
of Radicals
Answer:
Multiply.
Simplify
Answer: 24a
Simplify
Factor using squares.
Product Property
Multiply.
Combine like radicals.
Answer:
Simplify
Answer:
Simplify
F
O
I
L
Product Property
Answer:
Simplify
FOIL
Multiply.
Answer:
Subtract.
Simplify each expression.
a.
Answer:
b.
Answer: 41
Simplify
Multiply by
since
is the conjugate
of
FOIL
Difference of
squares
Multiply.
Answer:
Combine like terms.
Simplify
Answer:
Summary
A radical expression is in simplified form
when:
•The index n is as small as possible.
•The radicand contains no factors
(other than 1) that are nth powers of an
integer or polynomial.
•The radicand contains no fractions.
•No radicals appear in the denominator