Ejercicio 285

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CAPITULO XXXVI

Transformación de radicales dobles
Ejercicio 285
Transformar en suma algebraica de radicales simples:
  1. 5+ 24 Sea: a=5 b=24 m = a 2 b m = 5 2 24 m = 2524 m = 1 m =1 5+ 24 = a+m 2 + am 2 = 5+1 2 + 51 2 = 2 + 2 = 3 + 2
  2. 8 60 Sea: a=8 b=60 m = a 2 b m = 8 2 60 m = 6460 m = 4 m =2 8 60 = a+m 2 am 2 = 8+2 2 82 2 = 2 2 = 5 3
  3. 8+ 28 Sea: a=8 b=28 m = a 2 b m = 8 2 28 m = 6428 m = 36 m =6 8+ 28 = a+m 2 + am 2 = 8+6 2 + 86 2 = 2 + 2 2 = 7 +1
  4. 32 700 Sea: a=32 b=700 m = a 2 b m = 3 2 2 700 m = 1024700 m = 324 m =18 32 700 = a+m 2 am 2 = 32+18 2 3218 2 = 2 2 =5 7
  5. 14+ 132 Sea: a=14 b=132 m = a 2 b m = 1 4 2 132 m = 196132 m = 64 m =8 14+ 132 = a+m 2 + am 2 = 14+8 2 + 148 2 = 2 + 2 = 11 + 3
  6. 13+ 88 Sea: a=13 b=88 m = a 2 b m = 1 3 2 88 m = 16988 m = 81 m =9 13+ 88 = a+m 2 + am 2 = 13+9 2 + 139 2 = 2 + 2 = 11 + 2
  7. 11+2 30 = 11+ 120 Sea: a=11 b=120 m = a 2 b m = 1 1 2 120 m = 121120 m = 1 m =1 11+2 30 = a+m 2 + am 2 = 11+1 2 + 111 2 = 2 + 2 = 6 + 5
  8. 8418 3 = 84 972 Sea: a=84 b=972 m = a 2 b m = 8 4 2 972 m = 7056972 m = 6084 m =78 8418 3 = a+m 2 am 2 = 84+78 2 8478 2 = 2 2 =9 3
  9. 21+6 10 = 21+ 360 Sea: a=21 b=360 m = a 2 b m = 2 1 2 360 m = 441360 m = 81 m =9 21+6 10 = a+m 2 + am 2 = 21+9 2 + 219 2 = 2 + 2 = 15 + 6
  10. 28+14 3 = 28+ 588 Sea: a=28 b=588 m = a 2 b m = 2 8 2 588 m = 784588 m = 196 m =14 28+14 3 = a+m 2 + am 2 = 28+14 2 + 2814 2 = 2 + 2 = 21 + 7
  11. 144 6 = 14 96 Sea: a=14 b=96 m = a 2 b m = 1 4 2 96 m = 19696 m = 100 m =10 144 6 = a+m 2 am 2 = 14+10 2 1410 2 = 2 2 = 12 2 =2 3 2
  12. 55+30 2 = 55+ 1800 Sea: a=55 b=1800 m = a 2 b m = 5 5 2 1800 m = 30251800 m = 1225 m =35 55+30 2 = a+m 2 + am 2 = 55+35 2 + 5535 2 = 2 + 2 = 45 + 10 = 5. 3 2 + 10 =3 5 + 10
  13. 7312 35 = 73 5040 Sea: a=73 b=5040 m = a 2 b m = 7 3 2 5040 m = 53295040 m = 289 m =17 7312 35 = a+m 2 am 2 = 73+17 2 7317 2 = 2 2 = 45 28 = 5. 3 2 7. 2 2 =3 5 2 7
  14. 25360 7 = 253 25200 Sea: a=253 b=25200 m = a 2 b m = 25 3 2 25200 m = 6400925200 m = 38809 m =197 25360 7 = a+m 2 am 2 = 253+197 2 253197 2 = 2 2 =15 28 =15 7. 2 2 =152 7
  15. 29330 22 = 293 19800 Sea: a=293 b=19800 m = a 2 b m = 29 3 2 19800 m = 8584919800 m = 66049 m =257 29330 22 = a+m 2 am 2 = 293+257 2 293257 2 = 2 2 = 275 18 = 11. 5 2 2. 3 2 =5 11 3 2
  16. 5 6 + 2 3 Sea: a= 5 6 b= 2 3 m = a 2 b m = ( 5 6 ) 2 2 3 m = 25 36 2 3 m = 1 36 m = 1 6 5 6 + 2 3 = a+m 2 + am 2 = 5 6 + 1 6 2 + 5 6 1 6 2 = 1 2 + 4 2 = 1 2 + 1 3 = 1 2 2 2 + 1 3 3 3 = 2 2 + 3 3
  17. 3 4 1 2 Sea: a= 3 4 b= 1 2 m = a 2 b m = ( 3 4 ) 2 1 2 m = 9 16 1 2 m = 1 16 m = 1 4 3 4 1 2 = a+m 2 am 2 = 3 4 + 1 4 2 3 4 1 4 2 = 1 2 1 2 2 = 1 2 1 4 = 1 2 2 2 1 2 = 2 2 1 2 = 1 2 ( 2 1 )
  18. 9 16 + 1 8 Sea: a= 9 16 b= 1 8 m = a 2 b m = ( 9 16 ) 2 1 8 m = 81 256 1 8 m = 49 256 m = 7 16 9 16 + 1 8 = a+m 2 + am 2 = 9 16 + 7 16 2 + 9 16 7 16 2 = 1 2 + 1 8 2 = 1 2 + 1 16 = 1 2 2 2 + 1 4 = 2 2 + 1 4
    Hallar la raíz cuadrada de:
  19. 6+4 2 6+4 2 = 6+ 32 Sea: a=6 b=32 m = a 2 b m = 6 2 32 m = 3632 m = 4 m =2 6+4 2 = a+m 2 + am 2 = 6+2 2 + 62 2 = 2 + 2 =2+ 2
  20. 7+4 3 7+4 3 = 7+ 48 Sea: a=7 b=48 m = a 2 b m = 7 2 48 m = 4948 m = 1 m =1 7+4 3 = a+m 2 + am 2 = 7+1 2 + 71 2 = 2 + 2 =2+ 3
  21. 8+2 7 8+2 7 = 8+ 28 Sea: a=8 b=28 m = a 2 b m = 8 2 28 m = 6428 m = 36 m =6 8+2 7 = a+m 2 + am 2 = 8+6 2 + 86 2 = 2 + 2 2 = 7 +1
  22. 10+2 21 10+2 21 = 10+ 84 Sea: a=10 b=84 m = a 2 b m = 1 0 2 84 m = 10084 m = 16 m =4 10+2 21 = a+m 2 + am 2 = 10+4 2 + 104 2 = 2 + 2 = 7 + 3
  23. 18+6 5 18+6 5 = 18+ 180 Sea: a=18 b=180 m = a 2 b m = 1 8 2 180 m = 324180 m = 144 m =12 18+6 5 = a+m 2 + am 2 = 18+12 2 + 1812 2 = 2 + 2 = 15 + 3
  24. 242 143 242 143 = 24 572 Sea: a=24 b=572 m = a 2 b m = 2 4 2 572 m = 576572 m = 4 m =2 242 143 = a+m 2 am 2 = 24+2 2 242 2 = 2 2 = 13 11
  25. 3020 2 3020 2 = 30 800 Sea: a=30 b=800 m = a 2 b m = 3 0 2 800 m = 900800 m = 100 m =10 3020 2 = a+m 2 am 2 = 30+10 2 3010 2 = 2 2 = 20 10 = 5. 2 2 10 =2 5 10
  26. 9+6 2 9+6 2 = 9+ 72 Sea: a=9 b=72 m = a 2 b m = 9 2 72 m = 8172 m = 9 m =3 9+6 2 = a+m 2 + am 2 = 9+3 2 + 93 2 = 2 + 2 = 6 + 3
  27. 9824 5 9824 5 = 98 2880 Sea: a=98 b=2880 m = a 2 b m = 9 8 2 2880 m = 96042880 m = 6724 m =82 9824 5 = a+m 2 am 2 = 98+82 2 9882 2 = 2 2 = 90 8 = 10. 3 2 2. 2 2 =3 10 2 2