Transcript Simplifying Radicals - Flagstaff Arts and Leadership Academy

Simplifying Radicals
root
radicand
Perfect Cubes
Perfect Squares
1
64
4
81
9
100
16
121
25
144
36
169
49
196
225
400
625
1
216
8
343
27
512
64
729
125
1000
4
16
2
4

64
8

144
12
3
216
6
3
64
4
Find the largest Perfect Square Factor
8
20
LEAVE IN RADICAL FORM
4 2
2
4 5
4 5
2 2
2 5
4



16
4

75


25  3
25

32
16  2
5
3 

2
40
4  10
4
3
2
10
2 10
This time Prime Factor the radicand
80
48
2 2 2 2 5
LEAVE IN RADICAL FORM
2 2 2 2 3
2 2
4
2 2 5
3
3
50
5 5 2
5 2
4


5
450
5 5 332
5  3 2


15 2
x
y
2
yyyyyy
x x
x 
4
6
4x y
2
y y y
y3
4
px y
ppppxxxxxxyy
ppxxxy

2  2  x x  x  x  y  y
2xxy



2
2x y
p2 x 3 y
25c 8d10
5 c c c c d d d d d
5c 4 d 5

6 2

cows  (cows)

x
1
2
and
1
2 2
pigs  ( pigs )
2

2
y6
1
2 2
x 
4
px y
y 
y3
x




4
6
1
2 2
1
2
6
1
2
p x y 
1
6 2

6 2

p
4 
x
p2 x 3 y
y
2 
1
2


x
3
y
xxx
yyyyy
yy y
x x



5 7
yz
y y y y y zzzzzzz

y  y  z  z  z yz
2 3
y z
5
yz



y2 y
ab3z
abbbz
b abz
25c 4 d 3
55c c c c d d d
5 c c d d
 
5c 2 d d

4
32m n
2
22222m m m m n n


2 2  m  m  n 2
4m 2 n 2

To combine radicals: combine the ______________
coefficients
like
of __________
radicals
Simplify each expression
6 7 5 7 3 7  8 7
5 6 3 7 4 7 2 6  3 6 7 7
Simplify each expression:
Simplify each radical first (largest perfect square) and then combine.
2 50  3 32
2 25  2  3 16  2

2  5 2 3  4 2
10 2 12 2
2 2


Simplify each expression:
Simplify each radical first (largest perfect square) and then combine.
3 27  5 48
3 9  3  5 16  3
3  3 3 5  4 3

9 3  20 3


29 3
a
b 
ab
x a  y b  xy ab
radicands
To multiply radicals: multiply the _____________
and then multiply the _____________
.
coefficients
Simplify the remaining radicals.
Multiply and then simplify
5  35  175  25  7  5 7
2 8  3 7  6 56  6 4  14 



2 5  4 20  8 100 
6  2 14 12 14
8  10  80
 5 
5 5
25  5
7 


7  7
49  7
 8 
8 8
64  8
2
2
2




2
x
 x 
x
x 
2
x
a

b
a
b
To divide radicals:
coefficients
divide the____________,
if possible

radicands
divide the __________,
if possible
Rationalize
_________________
the denominator so that no
radical remains in the denominator
56

7
56

7
8
6 49

3 7
49
2 
7
2 7

222 2 2
225
15 225

 5 75  5 25  3  5  5 3  25 3
 5
3
3 3





Rationalizing the denominator.
6
7
This expression can not be
divided which leaves a radical
in the denominator.
We do not leave radicals in the
denominator.
So we need to rationalize
  by
multiplying the fraction by
something so we can eliminate

the radical in the denominator.


7

7
42

49
6
7
Look back at slide #15
42 cannot be simplified, so
we are finished.
42
7
This can be divided, but
this leaves a radical in the
denominator.
We do not radicals in the
denominator.
So we need to rationalize
by multiplying the fraction
by something so we can
eliminate the radical in
the
denominator.
1
5
5



2
10
10




1

2
2
2
2

2
3
12

3
12
12
12
This cannot be
divided which leaves
3 12
the radical in the
144


denominator.
 We do

not leave radicals in
3 4  3
the denominator. So
12

we need to
3 2 3
rationalize by
12
multiplying 
the
fraction by something Reduce the
6 3
so we can eliminate fraction.
12
the radical inthe
denominator.
3
2


Reduce the
 fraction.



3 3
36
3 3
6
3
2
3
3