Download Section 9.1

9.1
Radicals and Quadratic
Equations
By: Brian Levy
Honors Geometry
Period 9
Contents
•
Objective: Simplify radical expressions
and solve quadratic equations
1. Notes on Radicals
2. Practice with solving radical expressions
3. Practice with solving quadratic equations
Notes and Terms
• When a number is squared it is simply multiplied
by itself
– Ex. To find the square of 9 ….. 9X9 = 81
• To find the inverse of squaring a number, you
need to find its square root
–?So, what’s a square root?
Notes and Terms
• A square root of a number is one of the
two equal factors of that number
– The square root of a positive number will be
– 1. Positive (+)
– 2. Negative (-)
– Ex. Square root of 64 is 8…..8X8=64
– Ex. Square root of 64 is -8….(-8)X(-8)=64
Notes and Terms
• This is a radical sign
– It indicates that you are
supposed to find the
square root of a number
in terms of positive value.
81
• This is a radicand
5
– It is the number or
expression under the
radical sign.
Notes and Terms
• Radical Expression is any expression
having a term containing a radical sign
• Square root radicals are in simplest form
when:
– View Structure diagram on next slide
Notes and Terms
Square root radicals
In simplest form
No fraction appears
As a radical
No integral radicand
Has a square factor
Other than 1
No radical is in the
denominator
Notes and Terms
• Properties of Radicals
(if x > 0 and y > 0)
– 1.
xy 
 x  y 
xy
y
– 2.
x

y
– 3.
x y
x

y
y
Notes and Terms
• If you ever can’t find
the square root of a
number, remember
this helpful table
• Numbers on left
• Squares on right
• This is continuous
1
2
3
4
5
6
7
8
9
10
1
4
9
16
25
36
49
64
81
100
Let’s Practice
• Sample 1:
72 
72 

6
36 
2
36  2
2
Let’s Practice
• S2
4
4 6
2 6


6
3
6
• S3
2

3
6

9
6
3
Let’s Practice
• S4
3 18  2
3
2 2
9
9
19
50
2  10
25
2
2 
2
• S5-Simply square the
number outside the
radical sign. Then, times
it by the radicand, without
squaring he radicand.
7 2 7 2 
49  2 
98
Let’s Practice
• S6-Remember your brackets! Here’s an example
–x² = 28
x 4 7
x  2 7
 2
7

Let’s Practice
• S7
• z² - 5z = 6
• z² - 5z – 6 =0
to
to
solution
• (z+1) (z-6) =0
• z = -1 or z = 6
• {-1,6}
We can solve this
equation by using a
simple form of the
quadratic formula
It is crucial to set your
equation = to 0 and
remember brackets
group your final
Exercises for Practice
• Ex.1-Simplify
2 112
• Ex.3-Simplify
8  18  50
• Ex.2-Simplify
36
121
• Ex.4-Solve
• 9x² = 64
Exercises for Practice (Additional)
• The best all-around review for section 9.1
is in your 9.1 yellow radicals packet.
• On page 7, you will find 30 problems
consisting of radical expressions, square
roots, and quadratic equations.
• On page 8, you can check your work with
the answers Mr. Pricci has provided.
Answers
• Samples
S1 : 6
S2:
2
2
6
3
6
S3 :
3
S 4 : 19
2
S 5 : 98

S6 :  2
S 7 :  1,6
7


Answers
• Exercises
E1 : 8 7
E 2 : 10 2
6
E3 :
11
8  8
E4 :  ,
3 3

Works Cited
Brown, Richard G., et al. Algebra:
Structure and Method Book 1. Boston: Houghton Mifflin
Company, 1997.
Pricci, Vincent. “Radicals Notes.” Clarks Summit. 2008.
Rhoad, Richard, et al. Geometry for Enjoyment and
Challenge. Boston: McDougal Littell & Company, 1991.