Guia Radicales Dos
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LICEO DE APLICACIÓN DEPARTAMENTO DE MATEMÁTICA PROF.: XIMENA CASTRO
GUIA RADICALES DOS Nombre:
Curso: 3º Medio ___
I.- Reduzca términos semejantes: 2 +2 2 +3 2 =
1.
21.
1 3 1 1 12 − 18 + 48 + 72 = 2 3 4 6
22.
3 2 1 1 176 − 45 + 320 + 275 = 4 3 8 5
2. 3 3 − 5 3 − 6 3 + 9 3 = 5 − 3 5 − 11 5 + 2 5 =
3.
9x + 9 + 4x − 4 − 5 x − 1 =
4. 3 a − 4 a + 6 a − a =
23.
5. 3a 2 + 2a 2 − a 2 =
24. 2 m 2 n − 9m 2 n + 16mn 2 − 4mn 2 =
6.
3
p − 53 p + 23 p =
7. a b − 3a b + 5 a 2b − 4 a 4b 2 = 8.
1 2 3 1 a− a+ a− a= 2 5 4 3
9.
3 −2 2 +5 3 −6 2 + 2 =
25. 53 54 − 63 24 − 3 16 + 26. 27.
n
a 2n − 2 x a 4 x +
3p
13 2= 2
a6p =
1 2 3 21 ⋅ 42 ⋅ 22 = 2 3 7
28. 43
6
xy − 29
xy + 518 xy =
10. 4 6 − 3 5 − 5 6 + 2 5 = 11.
n
p − 2n p + 18n p − 4n p =
9 4 + = 5 5
29.
12. 3 7 + 2 28 − 6 63 =
30. 2 18 x 2 − 32 x 2 − 3 x 2 =
13. 11 2 + 3 813 12 =
31.
− 25 + − 144 =
32.
5 5 + = 18 12
33.
x+3 + x + 6x + 9
14. 3 3 − 22 75 − 5 27 = 15. 4 2 − 3 12 + 3 75 − 6 8 = 16. 2 20 + 125 + 45 =
2
17. - 4 28 + 63 + 6 20 + 2 45 =
3
34. 18. 7 8 + 4 75 − 2 32 + 27 = 1 3 19. 2 5 − 5+ 5= 2 4
20. 175 + 243 − 63 − 2 75 =
x−3 = x − 6x + 9 2
5
32a − 64b 15 ⎛ a − 2b ⎞ − ⎜ ⎟ = 2b − a ⎝ 2b − a ⎠
x− y x+ y − 35. 4 +2 x+ y x− y
36 x 2 = x2 − y2
LICEO DE APLICACIÓN DEPARTAMENTO DE MATEMÁTICA PROF.: XIMENA CASTRO
II.- Efectúa los siguientes productos: 3⋅ 2⋅ 6 =
1) 2)
3
20)
1 2 3 21 ⋅ 42 ⋅ 22 = 7 2 3
3x ⋅ 3 2 x ⋅ 3 16 x 2 =
2 ⋅3 2 ⋅4 2 =
21) 3)
4
2p3 ⋅ 4 5 p 7 ⋅ 4 7 p 6 = 22)
4)
2x + 1 ⋅ 2 x + 1 =
5)
a -1 ⋅ a −1 =
6)
6− 2⋅
7)
9)
23) 2 x ⋅ 5 4 x ⋅ 10
6+ 2 =
16 − 3 ⋅ 16 + 3 =
5+ 3⋅
8) 3
23 3 4m 2 ⋅ 5 16m 4 n = 4 3
5− 3 =
24)
a +b
25)
3p
26)
3x 2 yz ⋅ 3 9 x 4 y 2 z 5 =
( )( ) 11) ( 2 + 18 ) = 12) (3 2 + 2 3 ) =
29) (
2
(
14)
(
3− 5
) +(
30)
)
3+ 5 =
2 2 7 − 5 3 )( 7 + 5 3 ) = 7 7
9 5
15
x 19 ⋅ x =
)(
31) ( 2 + 3 + 7 )( 2 − 3 + 7 ) =
)
3x + 1 · 3x − 1 =
32 − 7 =
16)
x+ y⋅
x− y =
m n m · 6 m x − 1 ·n 2 3
32) 5 x 2 − 5 ⋅
4x + 4 = 5x − 5
33) 3 5 + 2 3 ⋅ 3 5 − 2 3 = 34) (7 12 − 6 3 ) 2 =
5x
x
=
)
4
35)
c2 ⋅ 5 c3 ⋅ 2 c4 c3 ⋅ 5 c2
18) 3 + 2 11 − 6 2 = 19)
x 11 ⋅ 3
2
32 + 7 ·
(
a x − 4 ⋅ x +1 a x + 6 =
2
15)
17) n
a4p =
28) (2 x + 1 − 4 x ) 2 =
2
13)
3p
27) (4 2 + 3 ) 2 =
10) 2 + 7 ⋅ 3 − 7 =
2
( a − b) 2 ⋅ a + b ( a − b) b =
a2p ⋅
x +1
1 = 16 x 2
=
53 15 ⋅ 123 50 = 6
II.- Efectúa las siguientes divisiones: 1.
50 : 2 =
3.
40c 2 ÷
c = 40
2. 20 24 ÷ 2 2 = 4.
3
54x 5 y15 : 3 2x 2 y 3 =
LICEO DE APLICACIÓN DEPARTAMENTO DE MATEMÁTICA PROF.: XIMENA CASTRO
5.
5m 6 n : 3 m 3 n 4 =
3
6.
16. (3 6 + 5 8 − 2 2 ) : 4 2 =
2 x +3 : 2 x =
17.
x 2 − 25 : x - 5 =
7.
3x
2 2a : 3 x 2 a -1 =
18. a 2 a 2 − 121 : a a - 11 =
8.
n
a m + 6 : n a m -6 =
19.
9.
5x
a 12 ÷ 5 x a 12−10 x =
20. ⎛⎜ x 2 − 4 : x - 2 ⎞⎟ : x + 2 =
10.
1 3 3xy : x= 4 2
11. 33 16a 5 : 43 2a 2 =
12. x y ÷
13.
x = y
13 1 13 1 : = 3 2 6 3
14. (12 20 − 18 15 ) : 6 5 =
a 2 − 6a + 9 : a - 3 =
⎝
⎠
21. ⎛⎜ 5 a 2 + 5 a 6 + 5 a 9 ⎞⎟ : 5 a 2 = ⎝
22.
3
⎠
a 4 b 4 3 bc −2 : + c5 a −1
23.
4
3 5 : 24 2 =
24.
3
3 2 :6 5 =
25.
1 1 2 x : 6 16 x 4 = 2 4
15. (30 6a − 27 18a + 18 12a ) : 6 6a =
Se ve difícil, pero no imposible!! SUERTE!
b3 a −1c −2 : = a −1c 4 b −1
GUIA RADICALES DOS Nombre:
Curso: 3º Medio ___
I.- Reduzca términos semejantes: 2 +2 2 +3 2 =
1.
21.
1 3 1 1 12 − 18 + 48 + 72 = 2 3 4 6
22.
3 2 1 1 176 − 45 + 320 + 275 = 4 3 8 5
2. 3 3 − 5 3 − 6 3 + 9 3 = 5 − 3 5 − 11 5 + 2 5 =
3.
9x + 9 + 4x − 4 − 5 x − 1 =
4. 3 a − 4 a + 6 a − a =
23.
5. 3a 2 + 2a 2 − a 2 =
24. 2 m 2 n − 9m 2 n + 16mn 2 − 4mn 2 =
6.
3
p − 53 p + 23 p =
7. a b − 3a b + 5 a 2b − 4 a 4b 2 = 8.
1 2 3 1 a− a+ a− a= 2 5 4 3
9.
3 −2 2 +5 3 −6 2 + 2 =
25. 53 54 − 63 24 − 3 16 + 26. 27.
n
a 2n − 2 x a 4 x +
3p
13 2= 2
a6p =
1 2 3 21 ⋅ 42 ⋅ 22 = 2 3 7
28. 43
6
xy − 29
xy + 518 xy =
10. 4 6 − 3 5 − 5 6 + 2 5 = 11.
n
p − 2n p + 18n p − 4n p =
9 4 + = 5 5
29.
12. 3 7 + 2 28 − 6 63 =
30. 2 18 x 2 − 32 x 2 − 3 x 2 =
13. 11 2 + 3 813 12 =
31.
− 25 + − 144 =
32.
5 5 + = 18 12
33.
x+3 + x + 6x + 9
14. 3 3 − 22 75 − 5 27 = 15. 4 2 − 3 12 + 3 75 − 6 8 = 16. 2 20 + 125 + 45 =
2
17. - 4 28 + 63 + 6 20 + 2 45 =
3
34. 18. 7 8 + 4 75 − 2 32 + 27 = 1 3 19. 2 5 − 5+ 5= 2 4
20. 175 + 243 − 63 − 2 75 =
x−3 = x − 6x + 9 2
5
32a − 64b 15 ⎛ a − 2b ⎞ − ⎜ ⎟ = 2b − a ⎝ 2b − a ⎠
x− y x+ y − 35. 4 +2 x+ y x− y
36 x 2 = x2 − y2
LICEO DE APLICACIÓN DEPARTAMENTO DE MATEMÁTICA PROF.: XIMENA CASTRO
II.- Efectúa los siguientes productos: 3⋅ 2⋅ 6 =
1) 2)
3
20)
1 2 3 21 ⋅ 42 ⋅ 22 = 7 2 3
3x ⋅ 3 2 x ⋅ 3 16 x 2 =
2 ⋅3 2 ⋅4 2 =
21) 3)
4
2p3 ⋅ 4 5 p 7 ⋅ 4 7 p 6 = 22)
4)
2x + 1 ⋅ 2 x + 1 =
5)
a -1 ⋅ a −1 =
6)
6− 2⋅
7)
9)
23) 2 x ⋅ 5 4 x ⋅ 10
6+ 2 =
16 − 3 ⋅ 16 + 3 =
5+ 3⋅
8) 3
23 3 4m 2 ⋅ 5 16m 4 n = 4 3
5− 3 =
24)
a +b
25)
3p
26)
3x 2 yz ⋅ 3 9 x 4 y 2 z 5 =
( )( ) 11) ( 2 + 18 ) = 12) (3 2 + 2 3 ) =
29) (
2
(
14)
(
3− 5
) +(
30)
)
3+ 5 =
2 2 7 − 5 3 )( 7 + 5 3 ) = 7 7
9 5
15
x 19 ⋅ x =
)(
31) ( 2 + 3 + 7 )( 2 − 3 + 7 ) =
)
3x + 1 · 3x − 1 =
32 − 7 =
16)
x+ y⋅
x− y =
m n m · 6 m x − 1 ·n 2 3
32) 5 x 2 − 5 ⋅
4x + 4 = 5x − 5
33) 3 5 + 2 3 ⋅ 3 5 − 2 3 = 34) (7 12 − 6 3 ) 2 =
5x
x
=
)
4
35)
c2 ⋅ 5 c3 ⋅ 2 c4 c3 ⋅ 5 c2
18) 3 + 2 11 − 6 2 = 19)
x 11 ⋅ 3
2
32 + 7 ·
(
a x − 4 ⋅ x +1 a x + 6 =
2
15)
17) n
a4p =
28) (2 x + 1 − 4 x ) 2 =
2
13)
3p
27) (4 2 + 3 ) 2 =
10) 2 + 7 ⋅ 3 − 7 =
2
( a − b) 2 ⋅ a + b ( a − b) b =
a2p ⋅
x +1
1 = 16 x 2
=
53 15 ⋅ 123 50 = 6
II.- Efectúa las siguientes divisiones: 1.
50 : 2 =
3.
40c 2 ÷
c = 40
2. 20 24 ÷ 2 2 = 4.
3
54x 5 y15 : 3 2x 2 y 3 =
LICEO DE APLICACIÓN DEPARTAMENTO DE MATEMÁTICA PROF.: XIMENA CASTRO
5.
5m 6 n : 3 m 3 n 4 =
3
6.
16. (3 6 + 5 8 − 2 2 ) : 4 2 =
2 x +3 : 2 x =
17.
x 2 − 25 : x - 5 =
7.
3x
2 2a : 3 x 2 a -1 =
18. a 2 a 2 − 121 : a a - 11 =
8.
n
a m + 6 : n a m -6 =
19.
9.
5x
a 12 ÷ 5 x a 12−10 x =
20. ⎛⎜ x 2 − 4 : x - 2 ⎞⎟ : x + 2 =
10.
1 3 3xy : x= 4 2
11. 33 16a 5 : 43 2a 2 =
12. x y ÷
13.
x = y
13 1 13 1 : = 3 2 6 3
14. (12 20 − 18 15 ) : 6 5 =
a 2 − 6a + 9 : a - 3 =
⎝
⎠
21. ⎛⎜ 5 a 2 + 5 a 6 + 5 a 9 ⎞⎟ : 5 a 2 = ⎝
22.
3
⎠
a 4 b 4 3 bc −2 : + c5 a −1
23.
4
3 5 : 24 2 =
24.
3
3 2 :6 5 =
25.
1 1 2 x : 6 16 x 4 = 2 4
15. (30 6a − 27 18a + 18 12a ) : 6 6a =
Se ve difícil, pero no imposible!! SUERTE!
b3 a −1c −2 : = a −1c 4 b −1
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