Ejercicio 249

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CAPITULO XXXI

R a d i c a l e s
Racionalización de expresiones conjugadas
Ejercicio 249
Racionalizar el denominador de:
  1. 3 2 + 3 5 = 3 ( 2 + 3 ) 5 × 2 + 3 + 5 ( 2 + 3 ) + 5 = 3 ( 2 + 3 + 5 ) ( 2 + 3 ) 2 (5 ) 2 = 6 + 3 2 + 15 2 +2 6 + 3 5 = 6 + 15 +3 2 6 = 6 + 15 +3 2 6 × 6 6 = 6 2 + 10. 3 2 +3 6 2( 6 ) = 6+3 10 +3 6 2( 6 ) = 3 (2+ 10 + 6 ) 2 = 2+ 10 + 6 4
  2. 2 2 + 3 + 6 = 2 ( 2 + 3 ) + 6 × 2 + 3 6 ( 2 + 3 ) 6 = 2 ( 2 + 3 6 ) ( 2 + 3 ) 2 (6 ) 2 = 2 2 + 6 3. 2 2 2+2 6 +36 = 2+ 6 2 3 2 6 1 × 2 6 +1 2 6 +1 = 4 6 +2( 6 ) 4 18 +2+ 6 2 3 (2 6 ) 2 1 = 5 6 +144 2. 3 3 2 3 4( 6 ) 1 = 5 6 12 2 2 3 +14 23
  3. 2 3 2+ 3 + 5 = 2 3 (2+ 3 ) + 5 × 2+ 3 5 (2+ 3 ) 5 = 4+ 2 3 2 5 2 3 3 2 + 15 (2+ 3 ) 2 (5 ) 2 = 42 5 3+ 15 2 2 +4 3 +35 = 15 2 5 +1 4 3 +2 × 4 3 2 4 3 2 = 4 45 8 15 +4 3 2 15 +4 5 2 (4 3 ) 2 2 2 = 4 5. 3 3 10 15 +4 3 +4 5 2 16( 3 ) 4 = 12 5 10 15 +4 3 +4 5 2 484 = 16 5 10 15 +4 3 2 44 = 2 (8 5 5 15 +2 3 1 ) = 8 5 5 15 +2 3 1 22
  4. 3 + 5 2 + 3 + 5 = 3 + 5 ( 2 + 3 ) + 5 × 2 + 3 5 ( 2 + 3 ) 5 = 6 + 3 2 15 + 10 + 15 5 2 ( 2 + 3 ) 2 (5 ) 2 = 6 +3+ 10 5 2 +2 6 + 3 5 = 6 + 10 2 2 6 × 6 6 = 6 2 + 60 2 6 2( 6 ) = 6+ 2 2 .15 2 6 2( 6 ) = 6+2 15 2 6 2( 6 ) = 2 (3+ 15 6 ) 2 ( 6 ) = 3+ 15 6 6
  5. 6 + 3 + 2 6 + 3 2 = 6 + 3 + 2 ( 6 + 3 ) 2 × 6 + 3 + 2 ( 6 + 3 ) + 2 = ( 6 + 3 + 2 ) 2 ( 6 + 3 ) 2 (2 ) 2 = 6+3+2+2 18 +2 12 +2 6 6+2 18 +32 = 11+2 2. 3 2 +2 3. 2 2 +2 6 7+2 2. 3 2 = 11+6 2 +4 3 +2 6 7+6 2 × 76 2 76 2 = 77+42 2 +28 3 +14 6 66 2 36 2 2 24 6 12 12 7 2 (6 2 ) 2 = 77+28 3 24 2 36( 2 ) 10 6 12 3. 2 2 4936( 2 ) = 77+28 3 24 2 7210 6 24 3 4972 = 5+4 3 24 2 10 6 23 = 10 6 4 3 +24 2 5 23
  6. 2 5 2 + 5 10 = 2 5 ( 2 + 5 ) 10 × 2 + 5 + 10 ( 2 + 5 ) + 10 = 2+ 10 + 20 10 5 50 ( 2 + 5 ) 2 (10 ) 2 = 3+ 5. 2 2 5 2 .2 2+2 10 +510 = 3+2 5 5 2 2 10 3 × 2 10 +3 2 10 +3 = 6 10 +4 50 10 20 9+6 5 15 2 (2 10 ) 2 3 2 = 6 10 +4 5 2 .2 10 5. 2 2 9+6 5 15 2 4( 10 ) 9 = 6 10 +20 2 20 5 9+6 5 15 2 31 = 5 2 6 10 14 5 9 31