Weitere ähnliche Inhalte
Mehr von Wollker Colares (16)
15 radiciação
- 1. 15
RADICIAÇÃO
01
3
=
3
. 5 = 3 5 = 3 5
5 5 5 52 5
7 7 7
02
2
=
2
.
35 = 2 35 =
2 35
7
32 7
32 7 7
35 37 7
5 2
= 2 2 =
2 . 3 . 5 2
=
6 6 6 .5 2 3 2
03 = .
5 2 5 2 5 2 5 2 5.5 . 2 5
04 a)
15
=
15
. 5 = 15 5 = 15 5 = 3 5
5 5 5 52 5
b)
2
=
2
. 3 = 2 3 = 2 3
3 3 3 3 2 3
2 7
= 2 2 =
7 . 2 7
=
7 7 7. 2 7 7
c) = .
2 7 2 7 2 7 2 7 2. 2 .7 2
3 3 3 3 3 3
d) 2 2
= 3 . 42 =
24
= = =
2
2 4 4
2 2
2 22 = 24 =
3
22
=
3
2
3 3 3 3
4 4 42 4 4 2 2 2 2
e)
5
=
5
.
20 = 5 20 = 5 22 . 5 = 2 . 5 5 = 5
20 20 20 20 2 20 2 . 2. 5 2
3 5
= 2 =
5 . 3 5
=
5 5 5. 3 5 5
f) = .
3 5 3 5 3 5 3 5
2 3.3 .5 3
5 3
= 2 =
2 . 3 . 5 3
=
6 6 6. 5 3 2 3
g) = .
53 5 3 5 3 5 3 2 5. 5.3 5
7 7 7 7
h) 10 10 5 53 10 . 5 53 2 . 5 . 5 54 2 54
= . = = =
7
5 54 5 54
7 7
5 53
7
52 5 7 5. 5. 5 5
05 3 3 5 − 2 = 3 5 − 2 = 3 5 − 2 = 5 − 2
= .
5 2 5 2 5 − 2 52 − 2 2 5−2
diferença de quadrados: o quadrado do primeiro menos o quadrado do segundo
- 2. 06
2
=
2
. 7 3 = 2 7 3 = 2 7 3 = 7 3
7 − 3 7 − 3 7 3 72 − 32 7−3 2
2 2 2 3 2 2 2 3
.
2 2 2 2 3
= = 2 2 =
2 2 − 3 2 2 − 3 2 2 3 2 2 − 32 22 . 2 − 3
07
2 2 2 3 2 2 2 3
=
4 . 2 − 3 5
08 1 1 5 2 = 1 5 2 = 5 2 = 5 2
= .
a) 5 − 2 5 − 2 5 2 52 − 2 2 5 − 2 3
b)
5
=
5
. 8 5 = 5 8 5 = 5 8 5 = 5 8 5
8 − 5 8 − 5 8 5 82 − 52 8 − 5 3
c)
4
=
4
. 7 − 3 = 4 7 − 3 = 4 7 − 3 = 7 − 3
7 3 7 3 7 − 3 72 − 32 7 − 3
3 3 3 2 3 3 2 3 3 2 3 3 2
d) = . = 2 = =
3 − 2 3 − 2 3 2 3 − 22 3 . 3 − 2 7
e)
4
=
4
.
2 3 2 = 4 2 3 2 = 42 3 2 =
2 3 − 2 2 3 − 2 2 3 2 2 2 32 − 22 22 . 3 − 2
4 2 3 2 2 2 3 2
=
10 5
5 4 2 − 2 3 5 4 2 − 2 3
.
5 5 4 2 − 2 3
f) = = 2 2 = 2
4 2 2 3 4 2 2 3 4 2 − 2 3 4 2 − 22 32 4 . 2 − 22 . 3
5 4 2 − 2 3 4 2 − 2 3 2 2 2 − 3 2 2 − 3
= = =
20 4 4 2
x x x
3 4 6
a2 , a3 , a2 Redução de
÷ = ÷ = ÷ = Radical ao
Mesmo Índice
12 12 12
m.m.c.
a 8
, a 9
, a4
- 3. EXERCÍCIOS DE APLICAÇÃO
01 a) 6
23 ,
6
3 2 d) 8
a4 ,
8
a 4 b6 , 8
ab
12 12 12 12 12 12
b) 24 , 33 , 42 e) x8 , x9 , x4
10 10 10 12 12
c) 25 , 22 , 21 f) a 6 , a8
02 a) 9 3 9
27 = 33 = 3 d) a2 b = a b
8 8
b) 34 = 3 e) a5 b4
4 5 5
c) 34 = 3 f) a5 . a . b5 . b2 = ab ab 2
03 a) 2 . 3 2 = 18 d) 3
3 . 33 = 81
3
3 4
b) 5 . 23 = 40
5
e) 2 . 24 = 32
4
6
c) 2 . 26 = 128
6
f) c . a 2 2 . b2 = a 4 b2 c
04 a) 3 . 52 = 5 3 d) 25 = 2 4 . 2 = 22 2 = 4 2
b) 22 . 32 . 5 = 2 . 3 5 = 6 5 e) a6 . a . b8 = a 3 b 4 a
3 3
c) 2 . 72 = 7 2 f) a3 . a 2 . b6 . b = ab 2 a2 b
05 a) 9 2
b) 8 5
Mesmo índice e radical (para poder somar e/ou subtrair)
3 Soma-se os números fora do radical
c) 6 5
d) 2 2
e) 25 − 2 . 5 2 2 . 72 − 2 . 3 2 = 22 2 − 5 2 7 2 − 3 2 = 3 2
3 3 3
f) 33 . 5 − 23 . 5 26 . 5 − 5 = 3 5 − 2 5 22 5 − 5 = 4 5
3 3 3 3 3 3
3 3 3
e) 23 . 6 − 3 4 26 . 3 3 = 2 3 − 3 3 22 3 3 = 4 3
3 3 3 3 3 3
f) 2 2 . 3 2 33 5 3 .
52 − 2 2 4 . 3 = 2 3 3 . 2 3 5 . 5 3 − 22 . 2 3 =
2 3 6 3 25 3 − 8 3 = 25 3
- 4. 06 a) 15
3
Mesmo índice (para poder multiplicar e/ou dividir)
b) 16 Multiplica-se os números de fora do radical e os r
2 radicandos (o de dentro da raiz)
c) 4 24
d) 24 60
6 6 6 6 6
e) 5 a 4 b 2 . 3 a 3 b 3 . 4 a 3 b4 = 5 . 3 . 4 a 4 3 3 . b 2 3 4 = 60 a 10 b9
f) 4 10 x 8 y 6 . 5 10 x 3 y 7 . 2 10 x5 y 5 = 4 . 5 . 2 10 x 8 3 5 . y 6 7 5 = 40 10 x 16 y 18
07 a) 4 = 2
3
b) 3
5
c) 4
d) 6
16
4 2 ÷ 63 = 6 216 =
6 2
27
10
e) a5 b5 ÷ a 4 b4 = 10 a 5 − 4
. b5 − 4 = 10
a . b
f) 18 ÷ 6 12 a 8 y 4 ÷ x6 y3 = 3 12 a 8 y 4 − 3 ÷ x 6 = 3 12 a 8 y ÷ x 6
08 2 3 − 33 3 3 . 5 2 = 2 3 − 3 3 3 . 5 3 = 14 3
09 2 3 = 2 . 3 3 . 2 = 6 6 = 6 6 =
3 2 3 3 2 2 3 2 22 3 2
2 6
=
3 6 5 6
6 6 6
2
10
625
10000
−
1
8 3
=
25
100
−
3 1
3 2
2
1 1
= − 2=
4 2
1−1
4
=
1
2
4 4 4
11 12 12 64 = 12 12 4 = 12 16 = 12 4 = 16 = 2
3 4 4
6 3 6 6 6 2
12 215 . 26 = 22 23 . 22 = 4 . 4 2 3 = 16 23 = 16 21 = 16 2
1 3
13
1
2
3 . 3 =3 ⇒
1
2
3 2
=
3
3
2
=3
3
2
−
1
2
=3 =3
2
2
1 1
2 2
3 3
- 5. 14
218 = 218 = 218
6 12 1
12
1
÷ 124 12 = 218 ÷ 124 = 1
0
4 3 12
124 124
15
2 2 2 . 2 = 2 2 2 . 2 = 2 2 . 2
2 4 2 4 2
8
. 2 4 = 2 2 . 2 2 . 24 =
15
2 . 28 2
. 2 4 . 28 =
16
2 . 22 . 2 4 . 28 =
16
215 = 2 16
16 3 2 − 2 2 . 32 3 23 . 32 = 3 2 − 2 . 3 2 3 . 2 . 3 2 =
3 2 − 6 2 18 2 = 15 2
17 17 − 15 = 2 = 2 . 32 = 64 = 4 = 1
17 15 32 32 32 32 2 32 4
18 a 2
b
. 4
b = a 2 b . b = 12 a 6 b3 . 12 b 3 = 12 a 6 b6
4
6
4
12 2 2
12 2 2
=
12
a 4 b4 = ab
3
ab
3
ab a b a b
19 x = 2
y= 2 . 72 − 25 − 2 2 . 2 ⇒ 7 2 − 2 2 2 − 2 2 ⇒ 2
x=y
20 x 3 6 12
x = x2 = 12 x−7 = 1
= 4 3
12 9 12 7
x . x 2
x x x
6 2 6 6 6
21 32 . 4 ⇒ 32 . 16 ⇒ 323 . 16 ⇒ 6 32 3 . 6 8 ⇒
A= 6 6 6
2 2 2
6 6 6
32 3 . 8 ⇒ 253 . 23 ⇒ 215 . 23 ⇒ 2 18 ⇒ 23 ⇒ 8
22 4
aa 3
= a . a
4 3 3
=
12
a 4 = 12 a 4
4
12 3
= 12
a = a 12
1
a a 1 a
23 3a 2
6a − 5 a = 3a 6a − 5a = 3a a =
4 2 8
2 4 4 2 2
4a 2 = 22 a 2 = 2a
24 31 10 − 83 − 2 = 31 10 − 81 = 31 10 − 9 = 31 1 =
5 6 5 6 5 6 5 6
5
32 = 2
25 1 6 5 4 = 1 6 9 = 1 6 3 = 1 9 =
1 3 = 4 = 2
- 6. 26 9 16 . 16 = 9 16 2
= 9 . 16 = 32 . 4 2 = 3 . 4 = 12
27 5
6 4 3 48
=
24
516 = 52 = 25
28 3 33 5 2 2 . 3 = 3 3 3 5 . 2 3 = 3 3 3 10 3 =
83 8 3 8 3
14 3 14 7
= =
8 3 8 4
12 12 12
29 2 2 2
3 2
. 28 = 2 2 2
3 4 10
= 2 2
3 4 10
. 24 = 2 2
3 8 14
12
= 2
3 8 14
12
. 28 =
12 12
24 222
= 2 11 = 211 = 2048
12
30 2 . 4 . 1 2 . 2 . 32 8 2 2 . 25 8 27 8 . 23 2 8 27 8 . 23 2
= = = = 5
= = 3 2
=
2 8 . 128 2 23 . 27 2 210 2. 2 2 210 2 .2 . 2
8 2
= 2
2. 4
2 . 5 2 10 2
31 2 . 3 3 . 3 = 6 9 = 6 . 3 10 = 18 10 = 28
2 2
32 a) 2 4 . 5 22 . 5 = 22 5 2 5 = 6 5
b) 3 5 32 . 5 − 2 22 . 5 = 3 5 3 5 − 2 . 2 5 = 2 5
c) 2 6 . 52 − 4 6 . 32 6 6 . 22 = 2 . 5 6 − 4 . 3 6 6 . 2 6 =
10 6 − 12 6 12 6 = 10 6
3 3
33 23 . 3 − 34
=
3 3
2 3 − 3 3
=
3
−1 3
= 12
3
− 3
=
3
− 3
=
12
22 3 5
. 92 226 5
. 92 25 . 9 2 . 26 25 . 322 . 26
6
211 . 3 4
12 12 12 12
− 34 − 3 4 2 . 38 − 2 . 312 −3 12 2
= −12 2
= . = =
12
211 . 3 4 12
2 11 . 34 12
2 . 38
12
212 . 312 2. 3 2