simplifying radicals - jugelmath.files.wordpress.com€¦ · 07/08/2016 · simplifying radicals...
TRANSCRIPT
Simplifying Radicals
To make some extra cash, Bill Shakespeare
works as a substitute math teacher.
Perfect Squares
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
256
324
400
625
289
361
4
16
25
100
144
= 2
= 4
= 5
= 10
= 12
8
20
32
75
40
=
=
=
=
=
2*4
5*4
2*16
3*25
10*4
=
=
=
=
=
22
52
24
35
102
Perfect Square Factor * Other Factor
LE
AV
E I
N R
AD
ICA
L F
OR
M
18
288
24
72
=
=
=
=
=
=
=
=
Perfect Square Factor * Other Factor
LE
AV
E I
N R
AD
ICA
L F
OR
M
2*9 23
2*144 212
6*4 62
2*36 26
+
To combine
radicals:
combine the
coefficients of
like radicals
Simplify each expression
737576 78
62747365 7763
Simplify each expression: Simplify each radical first and
then combine.
323502 2*1632*252
24*325*2
212210
22
Simplify each expression: Simplify each radical first and
then combine.
485273
22922029
34*533*3
3*1653*93
How much is 2 + 82
dollars?
= 2 + 4 ∗ 22
= 2 + 2 22
= 3 22= 32 2
2= 9 ∗ 2 = 18
Worksheet
Problems 1-10
*To multiply radicals:
multiply the
coefficients, then
multiply the radicands,
then simplify the
remaining radicals.
35*5 175 7*25 75
Multiply and then simplify
73*82 566 14*46
142*6 1412
204*52 1008 8010*8
2
5 5*5 25 5
2
7 7*7 49 7
2
8 8*8 64 8
2
x xx * 2x x
Worksheet
Problems 11-16
To divide radicals: divide the coefficients,
divide the radicands if possible, and
rationalize the denominator so that no
radical remains in the denominator
7
568 2*4 22
7
6This cannot be
divided which leaves
the 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*
7
6
49
42
7
42
42 cannot be
simplified, so we are
finished.
This can be divided
which leaves the
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.
10
5
2
2*
2
1
2
2
This cannot be
divided which leaves
the 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.
12
3
3
3*
12
3
36
33
6
33
2
3Reduce
the
fraction.
Worksheet
Problems 17-22