Simplifying Radicals. Perfect Squares 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 324 400...
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Transcript of Simplifying Radicals. Perfect Squares 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 324 400...
Simplifying Radicals
Perfect Squares
1
4
916
253649
64
81
100121
144169196
225
256
324
400
625
289
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
48
80
50
125
450
=
= =
=
=
3*16
5*16
2*25
5*25
2*225
=
=
=
=
=
34
54
225
55
215
Perfect Square Factor * Other Factor
LE
AV
E I
N R
AD
ICA
L F
OR
M
+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
22
212210
24*325*2
2*1632*252
Simplify each expression: Simplify each radical first and then combine.
485273
229
22029
34*533*3
3*1653*93
18
288
75
24
72
=
= =
=
=
=
=
=
=
=
Perfect Square Factor * Other Factor
LE
AV
E I
N R
AD
ICA
L F
OR
M
Simplify each expression
636556
547243
32782
Simplify each expression
20556
32718
6367282
*To multiply radicals: multiply the coefficients and then multiply the radicands and 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 10020 20010*20
2
5 5*5 25 5
2
7 7*7 49 7
2
8 8*8 64 8
2
x xx * 2x x
To divide radicals: divide the coefficients, divide the radicands if possible, and rationalize the denominator so that no radical remains in the denominator
7
56 8 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
10
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
6
3Reduce
the fraction.
2X
6Y
264 YXP
244 YX
10825 DC
= X
= Y3
= P2X3Y
= 2X2Y
= 5C4D10
3X
XX
=
=
XX *2
YY 45Y
=
= YY 2
33YPX
2712 YX
9825 DC
=
=
= 5Y
PXYYX *22
5Y
PXYXY=