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Lesson 4 1st

February 04, 2014

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
Lesson 4 1st

February 04, 2014

II. PERFECT SQUARES
The important thing about Perfect
S is that they are the squares
RE
A
of WHOLE NUMBERS!
U
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
Lesson 4 1st

February 04, 2014

III. Method for Simplifying Radicals
A. Completely factor the RADICAND
then match up pairs of the same factor
examples:

18

48

147

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Radicals

  • 1. Lesson 4 1st February 04, 2014 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 1st February 04, 2014 II. PERFECT SQUARES The important thing about Perfect S is that they are the squares RE A of WHOLE NUMBERS! U 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 1st February 04, 2014 III. Method for Simplifying Radicals A. Completely factor the RADICAND then match up pairs of the same factor examples: 18 48 147