EJERCICIOS DE RADICALES.

1.

a2 a2 + mn 2 m 2 n

2.

4a 2 cd + 8abcd + 4b 2 cd

3.

2ab 3 c 3 6a b c : 5 8 6 9a b c

4.

⎛ ⎞ 1 1 ⎜⎜ 2 ⎟⎟ (a + x ) − 2 ⎝ x (a − x ) a (a − x ) ⎠

2

4

3

1 ab 4

5.

3 ab + 4a 3b − 2 0,25 ab − a ab − 4

6.

5 6 64a 2 − 5 3 27a + 6 9 a 3

7.

2 3 a 6 b − 3a 2 3 64b + 5a 3 a 3 b + a 2 3 125b

8.

b a 2 c + 4 16a 6 b 4 c 2 − a 6 b 6 c 3

9.

98a 2 b 4 c 2 +

10.

a 3 mn + ab 2 n 2

ab 7 m 2 a 3b 5 mn

11. (a − b ) 3 (a + b )

12.

13.

14.

15.

16.

17.

250a 6 b 9 c 3 − 4 32a 8 b12 c 4 + 128a 6 b 2 c 4

3

4

(

− a2 + b2

1 ab 2 1 1 + 3b − 4 4a a a 3

)

(

a − b + a2 + b2

)

3

ab 2

8a 3 + 8a 4 + 1,5 3 27 + 27 a − 3 0,125 (1 + a ) a2m − a2n +

4

(m − n )2 b 4

+

6

(m − n )3 c 6

2a 2 b 0,18a a 18b 2 + + 2c 2 − 2 2 0,3 b b a c ac

8ab + cd a

72ab + 50ab − 288ab

a6 b2d − cd a

4a 4 c d 2 + c b2d

b 4c3 d3

a 3c 4 0,125

a + b + (a + b )

2

a−b

18. (2a + 3b ) 8a + (a + 2b − c ) 18a − (4a − b − 3c ) 2a

ab ⋅ 3 a 2 b 2 ⋅ 4 ab 3

19.

(

)(

20. 3 +

a 3− a

)

ab 3 a 2 b 4 a 3 c ⋅ ⋅ c b c2

34.

ac 5 4 bc b ⋅ ⋅ a c b4

6

21.

4

a2

6

ab 4

ab

b 2 10 a 7 b 9

5

22. a 2 ⋅ 2 a ⋅ a 3 2 ⋅ 2 3 a ⋅ a 6 2 ⋅ 2 6 a

)(

(

23. a + b +

a2 + b2 a + b − a2 + b2

3

24.

3

4

)

a a+ b

+

36.

5+ 3

4

a +4 b

1 m −4 n

b a− b

⎛⎛ a − b ⎞ a ⎞⎟ ⎟: b − − a ⋅b ⎟ ⎜⎜ a − 4 b ⎟ b ⎠ ⎝⎝ ⎠

38. ⎜ ⎜

bc

39.

a+b

27.

5− 3

+

1

37.

2a + 5 − 4a 2 − 8 ⋅ 2a + 5 + 2 a 2 − 2

26.

5− 3

a+b − a−b

a ⋅ 4 b ⋅8 c

) ( 41. ( 2a ⋅ 2a b ) 42. ((a + b ) a b (a − b ) 43. (a 2 ⋅ 2 bc ) 40. 3 4a b ⋅ 2ab 2

4

28.

29.

3

31.

2

3

2

x+ y x− y

4

3

2

3

5

3

2

3

a 2b

)

2

4

⎛ 5 a 4b3 a 5 a ⎞⎟ ⋅ ⋅ 44. ⎜ 4 ⎜ c b 2 c 3 b ⎟⎠ ⎝

1

2

1+ 2 + a

6 3

a

⎛⎛ a ⎞2 ⎛ 2 a ⎜ ⎟ :⎜ 45. ⎜ ⎜ ⎜ 3 b 2c ⎟ ⎜ 5 b 4c3 ⎠ ⎝ ⎝⎝

:8 a

a a ⋅9 a

46.

a 33.

3

5

2− a

4

32.

ab 2 5 a 4 c 4 6 b 5 d 2 10 c 2 d 6 ⋅ 3 2 ⋅ 2 2 ⋅ c2d b d a d a 4b8 a

30.

a2 b2 ⋅ b c

3

4 6m 1 3n 5 2m n ⋅ ⋅ 5 2n 2 8m 6 4m 3 n

25.

5+ 3

35.

:

3

a b

+

b a

− ab +

1 ab

47.

3

m 2 n ⎛⎜ 4 m 3 n 2 ⎝ a b − b a a

48.

m −1

ab m

ab

(

⎞ ⎟ ⎟ ⎠

m

3

3

⎞ ⎟ ⎟ ⎠

2

n

)

2 6

m 5 n 4 ⎞⎟ ⎠

2

49.

(

) ( ab ) 3

5

2ab ⋅

1

1 4

1 1 a 2 3

50.

64.

1

4

⎛3

51. ⎜⎜

⎞ a 2 b 3 ⎟⎟ ⎠

7

⎝

⎛

⎞ ⎟ ⎠ ⎟⎠

( ab ) ⎞⎟

⎛3 52. ⎜ 4 ⎜

5

⎜ ⎝ ⎝

6

65. 3

⎛ 2 ⎞ 55. ⎜ (1 + x ) 6 (1 + x ) ⎟ ⎝ ⎠

57.

a 5b 5

3

m 3 m2 6 m5

56.

a 3 2a 3 2a

3

⎛ ⎜ 58. ⎜ ⎜ ⎝

⎞ ⎛ m⎞ m ⎟ ⎜ ⎟ 5 ⎟ ⎜4n⎟ ⋅ n ⎟ ⎝ ⎠ ⎠ 2

3

4

59.

3

a 2 b 5 4 a 3b 7 a 5 b 5 a 7 b 3

60.

3

ab ab ⋅ 3 a 2 b 2 ⋅ a a ⋅

⎛ 61. ⎜ ⎜ ⎝

a b 3

62. 5

c ⎞⎟ d ⎟⎠

+

5

a7 ⋅ a 2

4

2

a3 ⋅ a5

⎛ ⎜ 3 a −2 b 3 63. ⎜ 5 4 2 − ⎜ 5 3 a b ⎝

⎞ ⎟ ⎟ ⎟ ⎠

−

1 4

2

−

1 2

⎛ − 14 ⎜a ⋅⎜ 2 ⎜ b− 5 ⎝

⎛ a2 ⎜⎜ − 2 ⎝b

a 4 b 6 a 3b 2

3

⎛ 15 12 ⎞ 3 ⎜a b ⎟ ⎜ ⎟ ⎝ ⎠

⎛ a −1 ⎞ ⎜⎜ − 2 ⎟⎟ ⎝b ⎠

2

abc 4 a 3 b 3 c 2 ⋅

53.

54.

8

⎛ 52 34 ⎞ 6 ⎜a b ⎟ ⎜ ⎟ ⎝ ⎠

a a

⎞ ⎟⎟ ⎠

−

3 2

⎞ ⎟ ⎟ ⎟ ⎠

−

3 4