44:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000 Números reales:@0.073089:0.043661:0.211864:0.043661:0.211864:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Cuando las expresiones numéricas tienen en el denominador una o más raíces, estas :@0.293660:0.136836:0.931236:0.136836:0.931236:0.120402:0.293660:0.120402:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 pueden ser eliminadas a través de un proceso llamado racionalización. De acuerdo con :@0.293660:0.153478:0.931483:0.153478:0.931483:0.137044:0.293660:0.137044:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la forma del denominador, analizaremos tres casos de racionalización.:@0.293660:0.170120:0.796695:0.170120:0.796695:0.153686:0.293660:0.153686:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Caso 1:@0.301224:0.202474:0.351012:0.202474:0.351012:0.185805:0.301224:0.185805:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 El denominador contiene un solo término formado por una sola raíz cuadrada. En este :@0.301224:0.229836:0.922997:0.229836:0.922997:0.213403:0.301224:0.213403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 caso, basta multiplicar numerador y denominador por la misma raíz cuadrada.:@0.301224:0.246478:0.865180:0.246478:0.865180:0.230044:0.301224:0.230044:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ejemplo 15:@0.293658:0.282092:0.378810:0.282092:0.378810:0.265422:0.293658:0.265422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Racionaliza la expresión obtenida como resultado en la situación inicial.:@0.293658:0.310175:0.810019:0.310175:0.810019:0.293741:0.293658:0.293741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Solución:@0.293658:0.338258:0.359792:0.338258:0.359792:0.321588:0.293658:0.321588:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 8:@0.307107:0.364650:0.316090:0.364650:0.316090:0.348217:0.307107:0.348217:0.000000 37:@0.298095:0.378624:0.325116:0.378624:0.325116:0.362191:0.298095:0.362191:0.000000:0.000000:0.000000:0.000000 :@0.329457:0.370760:0.352687:0.370760:0.352687:0.354326:0.329457:0.354326:0.000000:0.000000:0.000000 3:@0.333415:0.370205:0.348748:0.370205:0.348748:0.356490:0.333415:0.356490:0.000000 37:@0.357036:0.364650:0.384050:0.364650:0.384050:0.348217:0.357036:0.348217:0.000000:0.000000:0.000000:0.000000 37:@0.357036:0.378624:0.384050:0.378624:0.384050:0.362191:0.357036:0.362191:0.000000:0.000000:0.000000:0.000000 :@0.388399:0.370760:0.411629:0.370760:0.411629:0.354326:0.388399:0.354326:0.000000:0.000000:0.000000 5:@0.392356:0.370205:0.407690:0.370205:0.407690:0.356490:0.392356:0.356490:0.000000 8 37:@0.414298:0.364650:0.450215:0.364650:0.450215:0.348217:0.414298:0.348217:0.000000:0.000000:0.000000:0.000000:0.000000 37:@0.416170:0.378624:0.443186:0.378624:0.443186:0.362191:0.416170:0.362191:0.000000:0.000000:0.000000:0.000000 2:@0.443099:0.372560:0.448335:0.372560:0.448335:0.362980:0.443099:0.362980:0.000000 :@0.452885:0.370760:0.456916:0.370760:0.456916:0.354326:0.452885:0.354326:0.000000 5 :@0.456842:0.370205:0.476685:0.370205:0.476685:0.356490:0.456842:0.356490:0.000000:0.000000 8 37:@0.481059:0.364650:0.516977:0.364650:0.516977:0.348217:0.481059:0.348217:0.000000:0.000000:0.000000:0.000000:0.000000 37:@0.490066:0.378629:0.507957:0.378629:0.507957:0.362196:0.490066:0.362196:0.000000:0.000000 Multiplicamos el numerador y el denominador:@0.521363:0.370760:0.872916:0.370760:0.872916:0.354326:0.521363:0.354326:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 por 37 y aplicamos propiedades.:@0.293660:0.398838:0.537981:0.398838:0.537981:0.382404:0.293660:0.382404:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Caso 2:@0.301224:0.431191:0.351012:0.431191:0.351012:0.414522:0.301224:0.414522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Si el denominador de la fracción contiene dos términos en uno de los cuales o en los :@0.301224:0.458554:0.923908:0.458554:0.923908:0.442121:0.301224:0.442121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dos hay una raíz cuadrada, se multiplica el numerador y el denominador por el :@0.301224:0.475196:0.923442:0.475196:0.923442:0.458762:0.301224:0.458762:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 conjugado del denominador. El conjugado de una suma es la resta y viceversa. El :@0.301224:0.491838:0.923266:0.491838:0.923266:0.475404:0.301224:0.475404:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 producto que resulta, ( :@0.301224:0.508480:0.469881:0.508480:0.469881:0.492046:0.301224:0.492046:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.474839:0.508480:0.482294:0.508480:0.482294:0.492074:0.474839:0.492074:0.000000 1:@0.482221:0.507925:0.497554:0.507925:0.497554:0.494210:0.482221:0.494210:0.000000 )( :@0.497469:0.508480:0.527638:0.508480:0.527638:0.492046:0.497469:0.492046:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.506592:0.508480:0.514065:0.508480:0.514065:0.492074:0.506592:0.492074:0.000000 x:@0.532717:0.508480:0.540172:0.508480:0.540172:0.492074:0.532717:0.492074:0.000000 2:@0.540098:0.507925:0.555431:0.507925:0.555431:0.494210:0.540098:0.494210:0.000000 ), es igual a ( ) ( ) .:@0.555346:0.508480:0.743953:0.508480:0.743953:0.492046:0.555346:0.492046:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.564469:0.508480:0.571943:0.508480:0.571943:0.492074:0.564469:0.492074:0.000000 x:@0.668917:0.508480:0.676372:0.508480:0.676372:0.492074:0.668917:0.492074:0.000000 2:@0.681104:0.502416:0.686341:0.502416:0.686341:0.492835:0.681104:0.492835:0.000000 2:@0.690251:0.507925:0.705584:0.507925:0.705584:0.494210:0.690251:0.494210:0.000000 y:@0.723356:0.508480:0.730829:0.508480:0.730829:0.492074:0.723356:0.492074:0.000000 2:@0.735561:0.502416:0.740798:0.502416:0.740798:0.492835:0.735561:0.492835:0.000000 Ejemplo 16:@0.293660:0.546709:0.378812:0.546709:0.378812:0.530040:0.293660:0.530040:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Racionaliza :@0.293660:0.579217:0.378381:0.579217:0.378381:0.562783:0.293660:0.562783:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 6:@0.406138:0.573108:0.415121:0.573108:0.415121:0.556674:0.406138:0.556674:0.000000 5 3:@0.380993:0.587082:0.440266:0.587082:0.440266:0.570648:0.380993:0.570648:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.402964:0.586528:0.418297:0.586528:0.418297:0.572812:0.402964:0.572812:0.000000 Solución:@0.293660:0.607295:0.359794:0.607295:0.359794:0.590625:0.293660:0.590625:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Multiplicamos el numerador y el denominador por 5 3:@0.293660:0.635373:0.723886:0.635373:0.723886:0.618939:0.293660:0.618939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.686593:0.634818:0.701926:0.634818:0.701926:0.621102:0.686593:0.621102:0.000000 6:@0.321567:0.661771:0.330550:0.661771:0.330550:0.645338:0.321567:0.645338:0.000000 5 3:@0.296421:0.675745:0.355694:0.675745:0.355694:0.659312:0.296421:0.659312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.318393:0.675191:0.333726:0.675191:0.333726:0.661475:0.318393:0.661475:0.000000 :@0.358377:0.667880:0.379870:0.667880:0.379870:0.651446:0.358377:0.651446:0.000000:0.000000:0.000000 3:@0.360597:0.667325:0.375931:0.667325:0.375931:0.653609:0.360597:0.653609:0.000000 5 3:@0.381004:0.661771:0.440279:0.661771:0.440279:0.645338:0.381004:0.645338:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.402976:0.661217:0.418309:0.661217:0.418309:0.647501:0.402976:0.647501:0.000000 5 3:@0.381006:0.675745:0.440279:0.675745:0.440279:0.659312:0.381006:0.659312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.402976:0.675191:0.418309:0.675191:0.418309:0.661475:0.402976:0.661475:0.000000 :@0.443144:0.667880:0.447175:0.667880:0.447175:0.651446:0.443144:0.651446:0.000000 5:@0.445364:0.667325:0.460698:0.667325:0.460698:0.653609:0.445364:0.653609:0.000000 6( 5 3):@0.463698:0.661771:0.541475:0.661771:0.541475:0.645338:0.463698:0.645338:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.499368:0.661217:0.514701:0.661217:0.514701:0.647501:0.499368:0.647501:0.000000 5 :@0.481799:0.675751:0.494739:0.675751:0.494739:0.659317:0.481799:0.659317:0.000000:0.000000 2 :@0.494647:0.675196:0.514490:0.675196:0.514490:0.661480:0.494647:0.661480:0.000000:0.000000 3:@0.514398:0.675751:0.523381:0.675751:0.523381:0.659317:0.514398:0.659317:0.000000 :@0.544479:0.667880:0.565972:0.667880:0.565972:0.651446:0.544479:0.651446:0.000000:0.000000:0.000000 5:@0.546700:0.667325:0.562033:0.667325:0.562033:0.653609:0.546700:0.653609:0.000000 6( 5 3):@0.566595:0.661771:0.640419:0.661771:0.640419:0.645338:0.566595:0.645338:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.602264:0.661217:0.617598:0.661217:0.617598:0.647501:0.602264:0.647501:0.000000 2:@0.599003:0.675751:0.607986:0.675751:0.607986:0.659317:0.599003:0.659317:0.000000 3( 5 3) 3 5 3 3:@0.642765:0.667880:0.814447:0.667880:0.814447:0.651446:0.642765:0.651446:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.644986:0.667325:0.660319:0.667325:0.660319:0.653609:0.644986:0.653609:0.000000 2:@0.691951:0.667325:0.707285:0.667325:0.707285:0.653609:0.691951:0.653609:0.000000 5:@0.730016:0.667325:0.745349:0.667325:0.745349:0.653609:0.730016:0.653609:0.000000 2:@0.772183:0.667325:0.787517:0.667325:0.787517:0.653609:0.772183:0.653609:0.000000 Caso 3:@0.301224:0.705774:0.351012:0.705774:0.351012:0.689104:0.301224:0.689104:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Si el denominador solo tiene un término con una raíz de índice cualquiera, , se :@0.301224:0.733137:0.923352:0.733137:0.923352:0.716703:0.301224:0.716703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.884568:0.733137:0.894066:0.733137:0.894066:0.716731:0.884568:0.716731:0.000000 multiplica numerador y denominador por otra raíz de índice que complete una :@0.301205:0.749779:0.923336:0.749779:0.923336:0.733345:0.301205:0.733345:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m:@0.760614:0.749779:0.775229:0.749779:0.775229:0.733373:0.760614:0.733373:0.000000 potencia de exponente .:@0.301205:0.766421:0.487781:0.766421:0.487781:0.749987:0.301205:0.749987:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.475154:0.766421:0.484652:0.766421:0.484652:0.750015:0.475154:0.750015:0.000000 Ejemplo 17:@0.293640:0.799025:0.378792:0.799025:0.378792:0.782355:0.293640:0.782355:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Racionalizar :@0.293640:0.830811:0.383718:0.830811:0.383718:0.814377:0.293640:0.814377:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 8:@0.397454:0.824704:0.406436:0.824704:0.406436:0.808270:0.397454:0.808270:0.000000 5:@0.387720:0.832614:0.392956:0.832614:0.392956:0.823033:0.387720:0.823033:0.000000 6:@0.392909:0.838678:0.411015:0.838678:0.411015:0.822244:0.392909:0.822244:0.000000:0.000000:0.000000 3:@0.410934:0.832614:0.416171:0.832614:0.416171:0.823033:0.410934:0.823033:0.000000 :@0.420230:0.830813:0.424261:0.830813:0.424261:0.814380:0.420230:0.814380:0.000000 Solución:@0.293660:0.858891:0.359794:0.858891:0.359794:0.842222:0.293660:0.842222:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 El factor racionalizante es 6 porque completa el exponente 5.:@0.293660:0.886974:0.755089:0.886969:0.755089:0.870536:0.293660:0.870541:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.479893:0.880906:0.485130:0.880906:0.485130:0.871325:0.479893:0.871325:0.000000 2:@0.503108:0.880906:0.508345:0.880906:0.508345:0.871325:0.503108:0.871325:0.000000 8:@0.307532:0.916226:0.316515:0.916226:0.316515:0.899792:0.307532:0.899792:0.000000 5:@0.297798:0.924137:0.303035:0.924137:0.303035:0.914556:0.297798:0.914556:0.000000 6:@0.302989:0.930201:0.321094:0.930201:0.321094:0.913767:0.302989:0.913767:0.000000:0.000000:0.000000 3:@0.321013:0.924137:0.326250:0.924137:0.326250:0.914556:0.321013:0.914556:0.000000 :@0.330309:0.922335:0.353539:0.922335:0.353539:0.905901:0.330309:0.905901:0.000000:0.000000:0.000000 5:@0.334267:0.921780:0.349600:0.921780:0.349600:0.908065:0.334267:0.908065:0.000000 8:@0.367324:0.916226:0.376307:0.916226:0.376307:0.899792:0.367324:0.899792:0.000000 5:@0.357590:0.924137:0.362827:0.924137:0.362827:0.914556:0.357590:0.914556:0.000000 6:@0.362779:0.930201:0.380885:0.930201:0.380885:0.913767:0.362779:0.913767:0.000000:0.000000:0.000000 3:@0.380805:0.924137:0.386042:0.924137:0.386042:0.914556:0.380805:0.914556:0.000000 :@0.390101:0.922335:0.413331:0.922335:0.413331:0.905901:0.390101:0.905901:0.000000:0.000000:0.000000 3:@0.394058:0.921780:0.409392:0.921780:0.409392:0.908065:0.394058:0.908065:0.000000 5:@0.417382:0.910162:0.422619:0.910162:0.422619:0.900581:0.417382:0.900581:0.000000 6:@0.422571:0.916226:0.440677:0.916226:0.440677:0.899792:0.422571:0.899792:0.000000:0.000000:0.000000 2:@0.440597:0.910162:0.445834:0.910162:0.445834:0.900581:0.440597:0.900581:0.000000 5:@0.417385:0.924133:0.422622:0.924133:0.422622:0.914552:0.417385:0.914552:0.000000 6:@0.422571:0.930201:0.440677:0.930201:0.440677:0.913767:0.422571:0.913767:0.000000:0.000000:0.000000 2:@0.440597:0.924137:0.445834:0.924137:0.445834:0.914556:0.440597:0.914556:0.000000 :@0.449893:0.922335:0.453924:0.922335:0.453924:0.905901:0.449893:0.905901:0.000000 5 :@0.453850:0.921780:0.473693:0.921780:0.473693:0.908065:0.453850:0.908065:0.000000:0.000000 8 6:@0.483774:0.916226:0.515971:0.916226:0.515971:0.899792:0.483774:0.899792:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.492676:0.910162:0.497913:0.910162:0.497913:0.900581:0.492676:0.900581:0.000000 2:@0.515891:0.910162:0.521128:0.910162:0.521128:0.900581:0.515891:0.900581:0.000000 6:@0.497959:0.930201:0.506942:0.930201:0.506942:0.913767:0.497959:0.913767:0.000000 El conjugado de :@0.078581:0.187395:0.193088:0.187395:0.193088:0.172455:0.078581:0.172455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a x b:@0.078578:0.202524:0.124214:0.202524:0.124214:0.187609:0.078578:0.187609:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.086938:0.202524:0.090602:0.202524:0.090602:0.187584:0.086938:0.187584:0.000000 2:@0.101942:0.202019:0.115881:0.202019:0.115881:0.189550:0.101942:0.189550:0.000000 es :@0.124147:0.202524:0.157575:0.202524:0.157575:0.187584:0.124147:0.187584:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a x :@0.145533:0.202524:0.171926:0.202524:0.171926:0.187609:0.145533:0.187609:0.000000:0.000000:0.000000:0.000000 1:@0.171876:0.202019:0.185815:0.202019:0.185815:0.189550:0.171876:0.189550:0.000000 :@0.185732:0.202524:0.201411:0.202524:0.201411:0.187584:0.185732:0.187584:0.000000:0.000000:0.000000 b:@0.189329:0.202524:0.197747:0.202524:0.197747:0.187609:0.189329:0.187609:0.000000 y su producto es :@0.078585:0.217652:0.191503:0.217652:0.191503:0.202713:0.078585:0.202713:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a x b:@0.191338:0.217652:0.233398:0.217652:0.233398:0.202738:0.191338:0.202738:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.199698:0.212140:0.204459:0.212140:0.204459:0.203430:0.199698:0.203430:0.000000 2:@0.211125:0.217148:0.225065:0.217148:0.225065:0.204679:0.211125:0.204679:0.000000 2:@0.233345:0.212140:0.238105:0.212140:0.238105:0.203430:0.233345:0.203430:0.000000 .:@0.238062:0.217652:0.240974:0.217652:0.240974:0.202713:0.238062:0.202713:0.000000 El conjugado de :@0.078588:0.232781:0.193098:0.232781:0.193098:0.217842:0.078588:0.217842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a x b:@0.078588:0.247910:0.124214:0.247910:0.124214:0.232996:0.078588:0.232996:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.086938:0.247910:0.090602:0.247910:0.090602:0.232971:0.086938:0.232971:0.000000 2:@0.101942:0.247406:0.115881:0.247406:0.115881:0.234937:0.101942:0.234937:0.000000 y es :@0.124160:0.247910:0.173158:0.247910:0.173158:0.232971:0.124160:0.232971:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a x :@0.161136:0.247910:0.187509:0.247910:0.187509:0.232996:0.161136:0.232996:0.000000:0.000000:0.000000:0.000000 1:@0.187459:0.247406:0.201398:0.247406:0.201398:0.234937:0.187459:0.234937:0.000000 y :@0.201314:0.247910:0.236099:0.247910:0.236099:0.232971:0.201314:0.232971:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b:@0.204912:0.247910:0.213329:0.247910:0.213329:0.232996:0.204912:0.232996:0.000000 y su producto es: :@0.078583:0.263039:0.194346:0.263039:0.194346:0.248099:0.078583:0.248099:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a x b y:@0.194181:0.263039:0.247696:0.263039:0.247696:0.248125:0.194181:0.248125:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.202536:0.257527:0.207297:0.257527:0.207297:0.248817:0.202536:0.248817:0.000000 2:@0.213963:0.262535:0.227903:0.262535:0.227903:0.250066:0.213963:0.250066:0.000000 2:@0.236183:0.257527:0.240943:0.257527:0.240943:0.248817:0.236183:0.248817:0.000000 .:@0.247629:0.263039:0.250540:0.263039:0.250540:0.248099:0.247629:0.248099:0.000000 Competencia :@0.078581:0.145303:0.187141:0.145303:0.187141:0.128356:0.078581:0.128356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.078581:0.161945:0.176057:0.161945:0.176057:0.144998:0.078581:0.144998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000