Transcript Simplifying Radicals Perfect Squares16 121 36169 =2 =4 =5 = 10 144 = 12 LEAVE IN RADICAL FORM Perfect Square Factor * Other Factor = 4*2 = 2 2 = 4 *5 = 2 5 = 16*

Simplifying Radicals
Perfect Squares
1
64
225
4
81
256
9
16
100
121
289
25
36
49
144
169
196
400
324
625
4
=2
16
=4
25
=5
100
= 10
144 = 12
LEAVE IN RADICAL FORM
Perfect Square Factor * Other Factor
8
=
4*2
=
2 2
20
=
4 *5
=
2 5
32
=
16* 2 =
4 2
75
=
25* 3 = 5 3
40
=
4 *10 = 2 10
LEAVE IN RADICAL FORM
Perfect Square Factor * Other Factor
48
=
16 * 3 =
4 3
80
=
16 * 5 =
4 5
50
=
25* 2 = 25 2
125 =
25* 5 = 5 5
450 = 225* 2 = 15 2
×
To multiply radicals: multiply the
coefficients and then multiply the
radicands and then simplify the
remaining radicals.
Outside × Outside / Inside × Inside
Multiply and then simplify
5 * 35  175  25* 7  5 7
2 8 * 3 7  6 56  6 4 *14 
6 * 2 14  12 14
2 5 * 4 20 
 5
2

5* 5 
25  5

7* 7 
49  7

8* 8 
64  8

x* x 
x 
 7
2
 8
2
 x
2
2
x
To divide radicals:
divide the
coefficients, divide
the radicands if
possible, and
rationalize the
denominator so that
no radical remains in
the denominator
56

7
8
4*2  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.
6

7
6
*
7
42

49
7

7
42
7
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.
5

10
1
*
2
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.
3

12
3
*
12
3 3

36
Reduce
the
fraction.
3 3

6
3

3