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Chris Giovanello, LBUSD Math Curriculum Office, 2003
Radicals are rad!
Chris Giovanello, LBUSD Math Curriculum Office, 2003
I wonder if they can
be simplified?
Hmmmmm….
Chris Giovanello, LBUSD Math Curriculum Office, 2003
“Simplified” means that there are no perfect square factors in the
radicand.
Chris Giovanello, LBUSD Math Curriculum Office, 2003
Objective: Given 10 different
radicals, students will be able to
simplify at least 9 of them correctly.
Chris Giovanello, LBUSD Math Curriculum Office, 2003
Purpose:•To be able to compute radicals and express the answer in simplest radical form
•To do well on their assessmentsquizzes
chapter test
final exam
CRCT
Yeah! Way cool!
Chris Giovanello, LBUSD Math Curriculum Office, 2003
Prior knowledge:
Name the perfect squares from 1 to 400.
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
256
289
324
361
400
Chris Giovanello, LBUSD Math Curriculum Office, 2003
Why are they called perfect squares?
Because they are the areas of squares.
1
1
2
2
3
3
A = 1·1
A = 1 A = 2·2
A = 4 A = 3·3
A = 91 is a perfect
square 4 is a perfect square 9 is a perfect
square
Chris Giovanello, LBUSD Math Curriculum Office, 2003
Is 8 a perfect square?
Noooooo !
Chris Giovanello, LBUSD Math Curriculum Office, 2003
What symbol is used to represent square root?
Chris Giovanello, LBUSD Math Curriculum Office, 2003
81
Name the parts:
radical, radical sign,or
square root sign
Chris Giovanello, LBUSD Math Curriculum Office, 2003
81
Name the parts:
radicand
Chris Giovanello, LBUSD Math Curriculum Office, 2003
Simplify the following:
121
49 289
22511 15
7 17
Chris Giovanello, LBUSD Math Curriculum Office, 2003
What if the radicand is not a perfect square?
Huh?
Chris Giovanello, LBUSD Math Curriculum Office, 2003
1) Rewrite the radicand using prime factorization.
24That’s easy!
643222
Chris Giovanello, LBUSD Math Curriculum Office, 2003
2) Use the following theorem:
3222
baba
Why separate here?
2422 Because
3222
Chris Giovanello, LBUSD Math Curriculum Office, 2003
3) Replace the perfect square radicands with the whole number equivalent.
3222
322
62
Sikes!
Chris Giovanello, LBUSD Math Curriculum Office, 2003
62Is Simplified?
Yes! Because the radicand has no perfect square factors.
Chris Giovanello, LBUSD Math Curriculum Office, 2003
That was way easy! Give me another one to work
out.
50
Simplify:
Chris Giovanello, LBUSD Math Curriculum Office, 2003
50 105
255 255
25
Chris Giovanello, LBUSD Math Curriculum Office, 2003
Check for Understanding:
Thumbs upor
Thumbs down
To simplify a radical, first rewrite the radicand into
prime factorization.
Why?
Chris Giovanello, LBUSD Math Curriculum Office, 2003
Guided practice: Simplify the following radicals. Fold a paper into fourths. Number each section from 1 to 4. Put the answer to
each question in each of the sections. (Fill the section.)
72)3
90)2
28)1
300)4
26
103
72
310
On the count of 3, show me the answer to #1.
On the count of 3, show me the answer to #2.
On the count of 3, show me the answer to #3.
On the count of 3, show me the answer to #4.
Chris Giovanello, LBUSD Math Curriculum Office, 2003
You are now ready to add and
subtract radicals!
