Identifying the parts of a radical and simplifying a radical

1. Lesson 4 4th
February 05, 2014
PARTS OF A RADICAL
*
*If the _________ is not written, it is automatically a ____.
Lesson 4 - Simplifying Radicals
I. Basics of Radicals
**The term RADICAL - is the name of the symbol
index/root
4
3 4
8x y
RADICAND
3
24x y
When no index/root
is indicated it means
square root. Understood
2 is there.
2
Could be written
but it is accepted as
square root when
nothing is there.
3
8x
cube root
4
24x y

2. Lesson 4 4th
February 05, 2014
II. PERFECT SQUARES
The important thing about Perfect
S is that they are the squares
RE
of WHOLE NUMBERS!
UA
They are
SQ
They LITERALLY
'perfect'
describe the . . .
because there
are
AR EA
1
2
of
a
0.5
SQ UA RE
NO fractions
or decimals
Taking the square
root of a perfect
square will give
you the dimension
of one side of the
square.
BUT
the important
thing about
perfect-squares
is that they are
the squares of
WHOLE NUMBERS!
Perfect Squares
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
256
289
324
361
400
1 =1
256 =16
49 = 7
144 =12
289 =17
9 =3
64 = 8
169 =13
324 =18
16 = 4
81 = 9
196 =14
361 =19
25 = 5
24 = 476
2
25 = 625
121 =11
4 =2
2
36 = 6
100 =10
225 =15
400 =20

3. Lesson 4 4th
February 05, 2014
III. Method for Simplifying Radicals
A. Completely factor the RADICAND
then match up pairs of the same factor
examples:
18
48
147
more examples:
3 98
175x2
5
x y6z

4. Lesson 4 4th
February 05, 2014
Your turn!
72
8
1
2
4 3
288x y
3
3 225x
2
80x