Ejercicio 235

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CAPITULO XXXI

Radicales
Reducción al mínimo común índice
Ejercicio 235
Reducir al mínimo común índice:
  1. 5 , 23 m.c.m=6 5 = 5 1 2 = 5 3 6 = 5 3 6 = 756 23 = 2 1 3 = 2 2 6 = 2 2 6 = 46
  2. 2 , 34 m.c.m=4 2 = 2 1 2 = 2 2 4 = 2 2 4 = 44 34
  3. 3, 43 , 84 m.c.m=12 3 = 3 1 2 = 3 6 12 = 3 6 12 = 72912 43 = 4 1 3 = 4 4 12 = 4 4 12 = 25612 84 = 8 1 4 = 8 3 12 = 8 3 12 = 51212
  4. 2 , 33 , 54 , 76 m.c.m=12 2 = 2 1 2 = 2 6 12 = 2 6 12 = 6412 33 = 3 1 3 = 3 4 12 = 3 4 12 = 8112 54 = 5 1 4 = 5 3 12 = 5 3 12 = 7512 76 = 7 1 6 = 7 2 12 = 7 2 12 = 4912
  5. 5x , 4 x 2 y 3 , 7 a 3 b 6 m.c.m=6 5x = (5x ) 1 2 = (5x ) 3 6 = (5x ) 3 6 = 75 x 3 6 4 x 2 y 3 = (4 x 2 y ) 1 3 = (4 x 2 y ) 2 6 = (4 x 2 y ) 2 6 = 16 x 4 y 2 6 7 a 3 b 6
  6. 2ab 3 , 3 a 2 x 5 , 5 a 3 x 2 15 m.c.m=15 2ab 3 = (2ab ) 1 3 = (2ab ) 5 15 = (2ab ) 5 15 = 2 5 a 5 b 5 15 = 32 a 5 b 5 15 3 a 2 x 5 = (3 a 2 x ) 1 5 = (3 a 2 x ) 3 15 = (3 a 2 x ) 3 15 = 3 3 a 6 x 3 15 = 27 a 6 x 3 15 5 a 3 x 2 15
  7. 8 a 2 x 3 4 , 3 a 5 m 4 6 m.c.m=12 8 a 2 x 3 4 = (8 a 2 x 3 ) 1 4 = (8 a 2 x 3 ) 3 12 = (8 a 2 x 3 ) 3 12 = 8 3 a 6 x 9 12 = 512 a 6 x 9 12 3 a 5 m 4 6 = (3 a 5 m 4 ) 1 6 = (3 a 5 m 4 ) 2 12 = (3 a 5 m 4 ) 2 12 = 3 2 a 10 m 8 12 = 9 a 10 m 8 12
  8. x 2 3 , 2 y 3 6 , 5 m 7 9 m.c.m=18 x 2 3 = ( x 2 ) 1 3 = ( x 2 ) 6 18 = ( x 2 ) 6 18 = x 12 18 2 y 3 6 = (2 y 3 ) 1 6 = (2 y 3 ) 3 18 = (2 y 3 ) 3 18 = 2 3 y 9 18 = 8 y 9 18 5 m 7 9 = (5 m 7 ) 1 9 = (5 m 7 ) 2 18 = (5 m 7 ) 2 18 = 5 2 m 14 18 = 25 m 14 18
  9. 3a 4 , 2 b 2 5 , 7 x 3 10 m.c.m=20 3a 4 = (3a ) 1 4 = (3a ) 5 20 = (3a ) 5 20 = 3 5 a 5 20 = 243 a 5 20 2 b 2 5 = (2 b 2 ) 1 5 = (2 b 2 ) 4 20 = (2 b 2 ) 4 20 = 2 4 b 8 20 = 16 b 8 20 7 x 3 10 = (7 x 3 ) 1 10 = (7 x 3 ) 2 10 = (7 x 3 ) 2 20 = 7 2 x 6 20 = 49 x 6 20
  10. 2 a3 ,3 2b ,4 5 x 2 4 m.c.m=12 2 a3 =2 a 1 3 =2 a 4 12 =2 a 4 12 3 2b =3 (2b ) 1 2 =3 (2b ) 6 12 =3 (2b ) 6 12 =3 2 6 b 6 12 =3 64 b 6 12 4 5 x 2 4 =4 (5 x 2 ) 1 4 =4 (5 x 2 ) 3 12 =4 (5 x 2 ) 3 12 =4 5 3 x 6 12 =4 75 x 6 12
  11. 3 a 2 3 , 1 2 b 3 6 ,4 x 5 9 m.c.m=18 3 a 2 3 =3 ( a 2 ) 1 3 =3 ( a 2 ) 6 18 =3 a 12 18 1 2 b 3 6 = 1 2 ( b 3 ) 1 6 = 1 2 ( b 3 ) 3 18 = 1 2 b 9 18 4 x 5 9 =4 ( x 5 ) 1 9 =4 ( x 5 ) 2 18 =4 x 10 18
  12. 2m ,3 a 3 x 4 5 ,2 x 7 y 2 10 m.c.m=10 2m = (2m ) 1 2 = (2m ) 5 10 = (2m ) 5 10 = 2 5 m 5 10 = 32 m 5 10 3 a 3 x 4 5 =3 ( a 3 x 4 ) 1 5 =3 ( a 3 x 4 ) 2 10 =3 ( a 3 x 4 ) 2 10 =3 a 6 x 8 10 2 x 7 y 2 10