Download simplify radicals

GUIDED NQTES & PRACTICE
simplify radicals
square & cube roots
miss
jude
MATH!
what is a radical?
RADICAL EXPRESSIoNS
3 56  24xy
3
5 32
3 1
8
x2
what are perfect squares?
4
81  9
7
x
is the inverse of
3
x
is the inverse of
4
x
is the inverse of
5
x
is the inverse of
n
x
is the inverse of
2 3 2  3 16
what are perfect
cubes?
42  4
vocabulary we need to
know & use
decimal approximation:
give answer in exact form:
simplify a radical
Simplifying radicals
The square root of a number which is not a __________________ ____________ will
be an _________________ number. It is a decimal which does not repeat or terminate.
We can estimate a square root by deciding between which two
__________________ ________________ it falls.
0
1
2
3
4
5
6
7
8
9
10
12 is between ____ & ____
2 is between ____ & ____
82 is between ____ & ____
20 is between ____ & ____
8 is between ____ & ____
56 is between ____ & ____
29 is between ____ & ____
1
4
is between ____ & ____
40 is between ____ & ____
99 is between ____ & ____
50 is between ____ & ____
5
2
is between ____ & ____
write the decimal approximation to each indicated place value
square root
nearest tenth
nearest hundredth
nearest thousandth
40
2
66
5 7
3 19
evaluate each root below. If the root does not exist, write DNE.
81 =
400
3
4
81=
16  64=
8 =
8 =
=
3
8 =
3
36 + 3 1=
8
1=
2 225 =
1000=
3
125
3
81 =
0.04 =
0.027=
36 - 9=
144
121
3 1
64
=
=
900 =
6  49 =
1
64
=
25 =
5
32=
3 100 =
6 49 =
4
0=
Simplifying radicals
When we need an _____________ _____________ answer, we can’t use a
decimal approximation. The best we can do is to ____________________.
A fully simplified radical expression
has no _________________ _______________ factors.
We’ll start with whole numbers.
method 1: use the perfects
method 2: factor to the primes
review perfect square/cube chart.
factor out the perfect #.
bring the root to the outside.
factor completely. circle pairs/triples &
bring # to the outside. leave singles.
3
20 
200 
20 
200 
48 
63 
48 
63 
54 
3
-24 
3
54 
3
-24 
simplify each square root or cube root below.
16 
10 20 
3
3
16 
56 
72 
8 8
18 
48 
 99 
98 
4 3 64 
0.2 75 
9
16

81
100

3
250 
3
3
288 
128 
5000 
72 
24 
2 3 54 
275 
60 

8 50 
49
16
3
128 
6 75 
7 72 
0.5 3 256 
10 162 
operations with radicals
We can ________ or ____________ the _________ or ___________ by finding the
same way we combine like terms.
product/quotient of the
Add the __________________ of radicals
______________ and ____________ .
with the same ________ and _________.
Simplify if possible.
 3 2  5 2  
3 2  5 2 
3 75
5 3 2 7 
4 12
5
5 8 5 
600
96
=
12  72 - 48 

108
98
32
10 6  5 3  
2 8
4 72
=
20
8 5
3


48 
2

10 
-5 3 + 2 27=
6 75  12 

7 2  5 2  



75 7 20 =
2 5 4 5  
simplifying radicals with variables
we can also simplify radicals with variables in the radicand.
we’ll stick to square roots for now and factor by _________ __________.
(x)2 
(x 2 )2 
(x3 )2 
(x4 )2 
(x5 )2 
(x6 )2 
x2 
x4 
x6 
x8 
x10 
x12 
what pattern do you notice? ____________________________________________
Perfect squares have _____ exponents.
QUICKTIP: ________ the variable exponent by ___
The number __________ the decimal = the exponent of the variable _______
the number _________ the decimal = (0) no variable ___________
= (0.5) variable with power of one _________
to try together….
49x2 =
200b8 =
12hk3 =
4 50x 5 y 9 =
75m3n4 =
4n7m
243n3m11 =
try on your own….
275h10 
3 50xy4 z 
96x 7 y 8 
98a2b3c4 
2 2m4 18m4 =
15x 2 +x 2 
1000m8n3 
-5 36x 6 y 4 z 
-3 3w3 3w3 
simplifying radicals with variables
125k 3m4 =
121xy6 =
6x 4x 2 =
150y 8 
x15 y18 z12 
10x 3 8x 6 
5x 2 15x 2 
2y 2 2x 2 
- 3 3v =
-2
144x
=
4x
x8
=
625
-2b 3 320b5 
48n9 
49x3
=
100 x
-1
25x6
=
-16 9x 4 
10x - 16x2 
25 x
169x 3
=
-3w3 9w 
9 10
16
x 
50xy 4 z

2xy 2 z