Five-Minute Check (over Lesson 6–4)
CCSS
Then/Now
New Vocabulary
Key Concept: Product Property of Radicals
Example 1: Simplify Expressions with the Product Property
Key Concept: Quotient Property of Radicals
Example 2: Simplify Expressions with the Quotient Property
Concept Summary: Simplifying Radical Expressions
Example 3: Multiply Radicals
Example 4: Add and Subtract Radicals
Example 5: Multiply Radicals
Example 6: Real-World Example: Use a Conjugate to Rationalize a
Denominator
Over Lesson 6–4
A. 11h
B. 11h2
C. 13h2
D. –11h
Over Lesson 6–4
A.
B. –4ay3
C.
D. 8ay3
Over Lesson 6–4
A.
B.
C.
D.
Over Lesson 6–4
A. |m – 4|
B. m – 4
C. |m – 2|
D. m – 2
Over Lesson 6–4
A. about 1.43 m
B. about 2.52 m
C. about 3.11 m
D. about 5.48 m
Over Lesson 6–4
Between which two whole numbers is
A. 10 and 11
B. 11 and 12
C. 12 and 13
D. 13 and 14
?
Content Standards
A.SSE.2 Use the structure of an expression
to identify ways to rewrite it.
Mathematical Practices
1 Make sense of problems and persevere in
solving them.
You simplified expressions with nth roots.
• Simplify radical expressions.
• Add, subtract, multiply, and divide radical
expressions.
• rationalizing the denominator
• like radical expressions
• conjugate
Simplify Expressions with the Product Property
Factor into
squares where
possible.
Product Property
of Radicals
Simplify.
Answer:
Simplify Expressions with the Product Property
Factor into
cubes.
Product
Property of
Radicals
Simplify.
Answer:
A. Simplify
A.
B.
C.
D.
.
A.
B.
C.
D.
Simplify Expressions with the Quotient
Property
A.
Quotient Property
Factor into squares.
Product Property
Simplify Expressions with the Quotient
Property
Rationalize the
denominator.
Answer:
Simplify Expressions with the Quotient
Property
Quotient Property
Rationalize the
denominator.
Product Property
Simplify Expressions with the Quotient
Property
Multiply.
Answer:
A. Simplify
A.
B.
C.
D.
.
B. Simplify
A.
B.
C.
D.
Multiply Radicals
Product Property of
Radicals
Factor into cubes
where possible.
Product Property of
Radicals
= 5 ● 10 ● a or 50a
Answer: 5 ● 10 ● a or 50a
Multiply.
A. 12a
B. 24a
C. 4a
D. 6a
Add and Subtract Radicals
Factor using
squares.
Product Property
Multiply.
Combine like
radicals.
Answer:
A.
B.
C.
D.
Multiply Radicals
Simplify
.
F
O
I
L
Product Property
Answer:
Simplify
A.
B.
C.
D.
.
Use a Conjugate to Rationalize a
Denominator
GEOMETRY In a square with side a, the ratio of a
side to the difference between the diagonal and a
side is
. Use a conjugate to rationalize the
denominator and simplify
.
Use a Conjugate to Rationalize a
Denominator
Multiply.
Simplify.
Factor out the
GCF.
Use a Conjugate to Rationalize a
Denominator
Simplify.
GEOMETRY In the triangle shown with
height x, the ratio of the height to the
base is
. Use a conjugate to
rationalize the denominator and
simplify
.
A.
B.
C.
D.