Simpl ifying radicals
Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (215.95 KB, 23 trang )
Simplifying Radicals
Perfect Squares
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
256
289
324
400
625
4
=2
16
=4
25
=5
100
= 10
144 = 12
LEAVE IN RADICAL FORM
Perfect Square Factor * Other Factor
8
=
4*2
=
2
20
=
4*5
=
2 5
32
=
16 * 2 =
4
75
=
25 * 3 =
5 3
40
=
4 *10 = 2 10
2
2
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 =
450
=
225 * 2 = 15 2
5 5
+
To combine radicals: combine
the coefficients of like 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 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 and
then combine.
3 27 + 5 48 = 3 9 * 3 + 5 16 * 3 =
3*3 3 + 5* 4 3 =
9 2 + 20 2 =
29 2
LEAVE IN RADICAL FORM
Perfect Square Factor * Other Factor
18
=
=
288
=
=
75
=
=
24
=
=
72
=
=
Simplify each expression
6 5 +5 6 −3 6 =
3 24 + 7 54 =
2 8 − 7 32 =
Simplify each expression
6 5 + 5 20 =
18 + 7 32 =
2 28 − 7 + 6 63 =
*
To multiply radicals: multiply the
coefficients and then multiply
the radicands and then simplify
the remaining radicals.
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 = 20 100 = 20 *10 = 200
( 5)
2
( 7)
=
5* 5 =
25 =
=
7* 7 =
49 = 7
=
8* 8 =
64 = 8
=
x* x =
x =
2
( 8)
2
( x)
2
2
5
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
= 8=
7
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
10
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
3 3
=
36
Reduce
the
fraction.
3 3
=
6
3
6
X
Y
4
=X
2
= Y3
6
6
2
P X Y
4
4X Y
8
2
25C D
10
= P2X3Y
= 2X2Y
= 5C4D10
X
3
=
X
=
Y
5
2
X
*X
X
=
Y
=
2
Y
4
Y
Y
3
PX Y
=
3
2
X Y
= XY
7
12 X Y
8
2
9
=
25C D =
Y
Y
5
5
2
* PXY
PXY
