Ejercicio 238

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CAPITULO XXXI

R a d i c a l e s
Suma y Resta de radicales
Ejercicio 238
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  1. 45 27 20 = 3 2 .5 3 2 .3 2 2 .5 =3 5 3 3 2 5 = 5 (32 ) 3 3 = 5 3 3
  2. 175 + 243 63 2 75 = 5 2 .7 + 9 2 .3 3 2 .7 2 5 2 .3 =5 7 +9 3 3 7 10 3 = 7 (53 ) + 3 (910 ) =2 7 3
  3. 80 2 252 +3 405 3 500 = 4 2 .5 2 2 2 . 3 2 .7 +3 9 2 .5 3 5.1 0 2 =4 5 2.2.3 7 +3.9 5 3.10 5 =4 5 12 7 +27 5 30 5 = 5 (4+2730 ) 12 7 = 5 12 7
  4. 7 450 4 320 +3 80 5 800 =7 3 2 . 5 2 .2 4 2 6 .5 +3 4 2 .5 5 2 4 .2. 5 2 =7.3.5 2 4. 2 3 5 +3.4 5 5. 2 2 .5 2 =105 2 32 5 +12 5 100 2 = 2 (105100 ) + 5 (1232 ) =5 2 20 5
  5. 1 2 12 1 3 18 + 3 4 48 + 1 6 72 = 1 2 2 2 .3 1 3 3 2 .2 + 3 4 4 2 .3 + 1 6 2 2 .2. 3 2 = 1 2 . 2 3 1 3 . 3 2 + 3 4 . 4 3 + 1 6 . 2 . 3 2 = 3 2 +3 3 + 2 = 3 (1+3 ) + 2 ( 1 1 ) =4 3
  6. 3 4 176 2 3 45 + 1 8 320 + 1 5 275 = 3 4 4 2 .11 2 3 3 2 .5 + 1 8 2 6 .5 + 1 5 5 2 .11 = 3 4 . 4 11 2 3 . 3 5 + 1 8 . 2 3 5 + 1 5 . 5 11 =3 11 2 5 + 5 + 11 = 11 (3+1 ) + 5 (12 ) =4 11 5
  7. 1 7 147 1 5 700 + 1 10 28 + 1 3 2187 = 1 7 3. 7 2 1 5 2 2 . 5 2 .7 + 1 10 2 2 .7 + 1 3 3 6 .3 = 1 7 . 7 3 1 7 .2. 5 7 + 1 . 2 7 + 1 3 . 3 3 = 3 2 7 + 1 5 7 +9 3 = 3 (1+9 ) + 7 ( 1 5 2 ) =10 3 9 5 7
  8. 1 3 1 2 + 3 4 = 1.3 3.3 1.2 2.2 + 3 2 2 = 3 3 2 2 2 2 + 3 2 2 = 3 3 2 2 + 3 2 = 3 ( 1 3 + 1 2 ) 2 2 = 3 ( 2+3 6 ) 2 2 = 5 6 3 2 2
  9. 9 5 1 6 1 20 + 6 = 9.5 5.5 1.6 6.6 1.5 2 2 .5.5 + 6 = 3 2 .5 5 2 1.6 6 2 5 2 2 . 5 2 + 6 = 3 5 5 6 6 5 10 + 6 = 5 5 (3 1 2 ) + 6 (1 1 6 ) = 5 5 ( 61 2 ) + 6 ( 61 6 ) = 5 5 ( 5 2 ) + 6 ( 5 6 ) = 5 2 5 6 6
  10. 5 3 3 5 1 2 3 4 5 1 15 +3 1 12 = 5 3 3.5 5.5 1 2 3 2 2 5 1.15 15.15 +3 1.3 3. 2 2 .3 = 5 3 15 5 2 1 2 3 2 2 5 15 1 5 2 +3 3 3 2 . 2 2 = 5 3. 5 15 1 2.2 3 5 15 + 3 3 .2 3 = 1 3 15 1 4 3 1 3 15 + 1 2 3 = 15 ( 1 3 1 3 ) + 3 ( 1 2 1 4 ) = 3 ( 21 4 ) = 1 4 3
  11. 5 128 1 3 1 3 5 98 + 1 27 =5 2 6 .2 1 3 1.3 3.3 5 7 2 .2 + 1.3 3 3 .3 =5. 2 3 2 1 3 3 3 2 5.7 2 + 3 3 4 =40 2 1 3.3 3 35 2 + 1 3 2 3 = 2 (4035 ) =5 2
  12. 2 700 15 1 45 +4 5 16 56 1 7 =2 7.1 0 2 15 1.5 3 2 .5.5 +4 5 4 2 56 1.7 7.7 =2.10 7 15 5 3 2 . 5 2 + 4 . 1 4 5 56 7 7 2 =20 7 15 . 1 3 . 5 5 + 5 . 1 7 7 =20 7 5 + 5 8 7 = 7 (208 ) =12 7
  13. 25a x 2 + 49b 9a x 2 = 5 2 a x 2 + 7 2 b 3 2 a x 2 =5x a +7 b 3x a =x a (53 ) +7 b =2x a +7 b
  14. 2 m 2 n 9 m 2 n + 16m n 2 4m n 2 =2m n 3 2 m 2 n + 4 2 m n 2 2 2 m n 2 =2m n 3m n +4n m 2n m =2n m m n
  15. a 320x 7 5 a 2 x (a4b ) 5x =a 2 6 .5x 7a 5x (a4b ) 5x =a 2 6 .5x 7a 5x (a4b ) 5x =a. 2 3 5x 7a 5x (a4b ) 5x =8a 5x 7a 5x (a4b ) 5x = 5x [8a7a(a4b ) ] = 5x [ 8a 7a a +4b ] =4b 5x
  16. 9x9 + 4x4 5 x1 = 9(x1 ) + 4(x1 ) 5 x1 = 3 2 (x1 ) + 2 2 (x1 ) 5 x1 = 3 x1 + 2 x1 5 x1 =0
  17. 2 a 4 x+3 a 4 y a 2 9x+27y + 25 a 4 x+75 a 4 y =2 a 4 (x+3y ) a 2 9(x+3y ) + 25 a 4 (x+3y ) =2 a 2 x+3y a 2 3 2 (x+3y ) + 5 2 a 4 (x+3y ) =2 a 2 x+3y 3 a 2 x+3y +5 a 2 x+3y =4 a 2 x+3y
  18. 3a a+1 a 2 4a+4 +(a+1 ) 1 a+1 =3 a . 1 a a+1 4(a+1 ) +(a+1 ) 1 a+1 . a+1 a+1 =3 a+1 2 2 (a+1 ) +(a+1 ) a+1 (a+1 ) 2 =3 a+1 2 a+1 + (a+1 ). 1 a+1 a+1 =3 a+1 2 a+1 + a+1 =2 a+1
  19. (ab ) a+b ab (a+b ) ab a+b +(2a2b ) 1 ab =(ab ) a+b ab . ab ab (a+b ) ab a+b . a+b a+b +2(ab ) 1 ab . ab ab =(ab ) a 2 b 2 (ab ) 2 (a+b ) a 2 b 2 (a+b ) 2 +2(ab ) ab (ab ) 2 = (ab ). 1 ab a 2 b 2 (a+b ). 1 a+b a 2 b 2 +2 (ab ). 1 ab ab = a 2 b 2 a 2 b 2 +2 ab =2 ab