Algebra 1 Notes 9.1.notebook
How can you multiply and divide square roots?
April 28, 2015
Algebra 1 Notes 9.1.notebook
Before we...
April 28, 2015
9.1 Properties of Radicals
Learned to solve some roots.
Today we will...
Use properties/rationalizing to
simplify expressions. Perform
operations with radicals.
Why?
Figure out the height of the
Parthenon in Greece.
Summary...
Assign: Pg.723
3-8,10,12,13,16-18,22,25,27,36,37
Algebra 1 Notes 9.1.notebook
April 28, 2015
Algebra 1 Notes 9.1.notebook
April 28, 2015
Algebra 1 Notes 9.1.notebook
a. = April 28, 2015
Factor using the greatest perfect square factor.
= Product Property of Square Roots
= Simplify.
b. = Factor using the greatest perfect square factor.
= Product Property of Square Roots
= Simplify.
Algebra 1 Notes 9.1.notebook
April 28, 2015
Simplify the expression.
1. 2. 3. 4. Algebra 1 Notes 9.1.notebook
April 28, 2015
Algebra 1 Notes 9.1.notebook
a. = Quotient Property of Square Roots
= Simplify.
b. = Quotient Property of Square Roots
= Simplify.
April 28, 2015
Algebra 1 Notes 9.1.notebook
April 28, 2015
a. = Factor using the greatest perfect cube factor.
= Product Property of Cube Roots
= Simplify.
b. = Factor using the greatest perfect cube factors.
= Product Property of Cube Roots
= Simplify.
c. = Quotient Property of Cube Roots
= Simplify.
d. = Quotient Property of Cube Roots
= Factor using the greatest perfect cube factors.
= Product Property of Cube Roots
= Simplify.
Algebra 1 Notes 9.1.notebook
April 28, 2015
Simplify the expression.
5.
6.
7.
9.
10.
11.
8. 12.
Algebra 1 Notes 9.1.notebook
April 28, 2015
Now what?
Algebra 1 Notes 9.1.notebook
April 28, 2015
Rationalizing the denominator
Algebra 1 Notes 9.1.notebook
April 28, 2015
Algebra 1 Notes 9.1.notebook
April 28, 2015
a. = Multiply by .
= Product Property of Square Roots
= Product Property of Square Roots
= Simplify.
b. = Multiply by .
= Product Property of Cube Roots
= Simplify.
Algebra 1 Notes 9.1.notebook
April 28, 2015
Conjugates
conjugate
Algebra 1 Notes 9.1.notebook
Simplify .
April 28, 2015
Algebra 1 Notes 9.1.notebook
April 28, 2015
Simplify the expression.
13.
14.
15.
16.
17.
18.
19.
20.
Algebra 1 Notes 9.1.notebook
April 28, 2015
Algebra 1 Notes 9.1.notebook
April 28, 2015
Algebra 1 Notes 9.1.notebook
April 28, 2015
Performing Operations w/Radicals
a) Adding and Subtracting
Radicals with the same index and radicand are called like
radicals. You can add and subtract like radicals by adding/
subtracting their coefficients.
EX:
5√7 + √11 - 8√7
b) Multiplying
You multiply by using the distributive property. Multiply the
coefficients together and multiply the radicands together.
Simplify the final product.
EX:
√3(8√2 - 7√32)
Algebra 1 Notes 9.1.notebook
a.
April 28, 2015
Commutative Property of Addition
Distributive Property
Subtract.
b.
Factor using the greatest perfect
square factor.
Product Property of Square Roots
Simplify.
Distributive Property
Add.
c.
Distributive Property
Add.
Algebra 1 Notes 9.1.notebook
Simplify .
April 28, 2015
Algebra 1 Notes 9.1.notebook
April 28, 2015
Simplify the expression.
23.
24.
25.
26.
27.
28.
Algebra 1 Notes 9.1.notebook
Pg.487
76-82 even (Adding/Subtracting)
83-86 (Multiplying)
April 28, 2015