32:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000
Conjuntos numéricos: reales y complejos:@0.073089:0.043661:0.435822:0.043661:0.435822:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5.2 Racionalización de binomios :@0.293660:0.136836:0.549941:0.136836:0.549941:0.119889:0.293660:0.119889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 3:@0.293660:0.164198:0.370032:0.164198:0.370032:0.147529:0.293660:0.147529:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Observemos ejemplos de racionalización de binomios.:@0.293660:0.184418:0.693771:0.184418:0.693771:0.167984:0.293660:0.167984:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a.:@0.322118:0.218173:0.334800:0.218173:0.334800:0.201504:0.322118:0.201504:0.000000:0.000000
 :@0.334802:0.218167:0.338520:0.218167:0.338520:0.200984:0.334802:0.200984:0.000000
. Para obtener un número o expresión sin radical en el denominador, :@0.425883:0.218167:0.930916:0.218167:0.930916:0.201733:0.425883:0.201733:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
multiplica el numerador y el denominador por la conjugada del denominador, :@0.350572:0.240855:0.930934:0.240855:0.930934:0.224421:0.350572:0.224421:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en este caso, por   :@0.350572:0.263544:0.485330:0.263544:0.485330:0.247110:0.350572:0.247110:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.380874:0.309973:0.396783:0.309973:0.396783:0.291655:0.380874:0.291655:0.000000
:@0.422108:0.298317:0.438018:0.298317:0.438018:0.280000:0.422108:0.280000:0.000000
:@0.463725:0.309973:0.479635:0.309973:0.479635:0.291655:0.463725:0.291655:0.000000
:@0.503604:0.298317:0.509964:0.298317:0.509964:0.280000:0.503604:0.280000:0.000000
:@0.534048:0.289007:0.549957:0.289007:0.549957:0.270690:0.534048:0.270690:0.000000
:@0.534048:0.309973:0.549957:0.309973:0.549957:0.291655:0.534048:0.291655:0.000000
2:@0.381466:0.288403:0.390786:0.288403:0.390786:0.271352:0.381466:0.271352:0.000000
7:@0.367199:0.309368:0.376519:0.309368:0.376519:0.292317:0.367199:0.292317:0.000000
3:@0.407192:0.309368:0.416512:0.309368:0.416512:0.292317:0.407192:0.292317:0.000000
2:@0.464317:0.288403:0.473638:0.288403:0.473638:0.271352:0.464317:0.271352:0.000000
7:@0.450050:0.309368:0.459371:0.309368:0.459371:0.292317:0.450050:0.292317:0.000000
3:@0.490044:0.309368:0.499364:0.309368:0.499364:0.292317:0.490044:0.292317:0.000000
7:@0.524817:0.288005:0.534137:0.288005:0.534137:0.270954:0.524817:0.270954:0.000000
3:@0.564810:0.288005:0.574130:0.288005:0.574130:0.270954:0.564810:0.270954:0.000000
7:@0.524817:0.309201:0.534137:0.309201:0.534137:0.292149:0.524817:0.292149:0.000000
3:@0.564810:0.309201:0.574130:0.309201:0.574130:0.292149:0.564810:0.292149:0.000000
número:@0.366494:0.322327:0.399435:0.322327:0.399435:0.312461:0.366494:0.312461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
irracional:@0.366284:0.330666:0.405124:0.330666:0.405124:0.320801:0.366284:0.320801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.574789:0.296169:0.577992:0.296169:0.577992:0.279735:0.574789:0.279735:0.000000
 :@0.322121:0.360302:0.326152:0.360302:0.326152:0.343868:0.322121:0.343868:0.000000
Utiliza el :@0.350579:0.360302:0.416385:0.360302:0.416385:0.343868:0.350579:0.343868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
producto notable (  +  )(  –  ) =  ² –  ² para obtener el resultado del :@0.416599:0.360302:0.930990:0.360302:0.930990:0.343868:0.416599:0.343868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.555408:0.360302:0.564667:0.360302:0.564667:0.343896:0.555408:0.343896:0.000000
b a b:@0.584142:0.360302:0.639382:0.360302:0.639382:0.343896:0.584142:0.343896:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.663735:0.360302:0.672993:0.360302:0.672993:0.343896:0.663735:0.343896:0.000000
b:@0.695966:0.360302:0.705225:0.360302:0.705225:0.343896:0.695966:0.343896:0.000000
denomin:@0.350572:0.376944:0.417961:0.376944:0.417961:0.360510:0.350572:0.360510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ador.:@0.417961:0.376944:0.453929:0.376944:0.453929:0.360510:0.417961:0.360510:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.293660:0.533101:0.297691:0.533101:0.297691:0.516667:0.293660:0.516667:0.000000
(:@0.633982:0.412052:0.640854:0.412052:0.640854:0.379541:0.633982:0.379541:0.000000
):@0.710259:0.412052:0.717131:0.412052:0.717131:0.379541:0.710259:0.379541:0.000000
( ) ( ):@0.613055:0.440068:0.718782:0.440068:0.718782:0.407557:0.613055:0.407557:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.445415:0.482641:0.452287:0.482641:0.452287:0.450130:0.445415:0.450130:0.000000
) (:@0.521692:0.482641:0.567384:0.482641:0.567384:0.450130:0.521692:0.450130:0.000000:0.000000:0.000000
):@0.636789:0.482641:0.643661:0.482641:0.643661:0.450130:0.636789:0.450130:0.000000
:@0.379294:0.430532:0.396485:0.430532:0.396485:0.412570:0.379294:0.412570:0.000000
:@0.425729:0.419103:0.442920:0.419103:0.442920:0.401141:0.425729:0.401141:0.000000
:@0.470698:0.430532:0.487890:0.430532:0.487890:0.412570:0.470698:0.412570:0.000000
:@0.515668:0.419103:0.522540:0.419103:0.522540:0.401141:0.515668:0.401141:0.000000
:@0.548564:0.409960:0.565756:0.409960:0.565756:0.391998:0.548564:0.391998:0.000000
:@0.552321:0.430532:0.569512:0.430532:0.569512:0.412570:0.552321:0.412570:0.000000
:@0.594999:0.419103:0.612191:0.419103:0.612191:0.401141:0.594999:0.401141:0.000000
:@0.669997:0.406348:0.687188:0.406348:0.687188:0.388386:0.669997:0.388386:0.000000
:@0.664425:0.434370:0.681616:0.434370:0.681616:0.416408:0.664425:0.416408:0.000000
:@0.414378:0.489680:0.431569:0.489680:0.431569:0.471718:0.414378:0.471718:0.000000
:@0.479573:0.476939:0.496764:0.476939:0.496764:0.458977:0.479573:0.458977:0.000000
:@0.475879:0.500389:0.493070:0.500389:0.493070:0.482427:0.475879:0.482427:0.000000
:@0.531332:0.489680:0.548523:0.489680:0.548523:0.471718:0.531332:0.471718:0.000000
:@0.592770:0.476939:0.609962:0.476939:0.609962:0.458977:0.592770:0.458977:0.000000
:@0.648307:0.489680:0.665498:0.489680:0.665498:0.471718:0.648307:0.471718:0.000000
:@0.691377:0.480537:0.708569:0.480537:0.708569:0.462575:0.691377:0.462575:0.000000
2:@0.383690:0.409353:0.393761:0.409353:0.393761:0.392633:0.383690:0.392633:0.000000
7:@0.368294:0.429925:0.378365:0.429925:0.378365:0.413205:0.368294:0.413205:0.000000
3:@0.411510:0.429925:0.421581:0.429925:0.421581:0.413205:0.411510:0.413205:0.000000
2:@0.473237:0.409353:0.483308:0.409353:0.483308:0.392633:0.473237:0.392633:0.000000
7:@0.457821:0.429925:0.467892:0.429925:0.467892:0.413205:0.457821:0.413205:0.000000
3:@0.501036:0.429925:0.511107:0.429925:0.511107:0.413205:0.501036:0.413205:0.000000
7:@0.537565:0.409353:0.547636:0.409353:0.547636:0.392633:0.537565:0.392633:0.000000
3:@0.580780:0.409353:0.590851:0.409353:0.590851:0.392633:0.580780:0.392633:0.000000
7:@0.537565:0.429925:0.547636:0.429925:0.547636:0.413205:0.537565:0.413205:0.000000
3:@0.580780:0.429925:0.590851:0.429925:0.590851:0.413205:0.580780:0.413205:0.000000
2:@0.623335:0.405741:0.633406:0.405741:0.633406:0.389021:0.623335:0.389021:0.000000
7:@0.655241:0.405741:0.665312:0.405741:0.665312:0.389021:0.655241:0.389021:0.000000
3:@0.698436:0.405741:0.708507:0.405741:0.708507:0.389021:0.698436:0.389021:0.000000
7:@0.634294:0.433763:0.644365:0.433763:0.644365:0.417043:0.634294:0.417043:0.000000
3:@0.700087:0.433763:0.710158:0.433763:0.710158:0.417043:0.700087:0.417043:0.000000
2:@0.434768:0.476332:0.444839:0.476332:0.444839:0.459612:0.434768:0.459612:0.000000
7:@0.466674:0.476332:0.476745:0.476332:0.476745:0.459612:0.466674:0.459612:0.000000
3:@0.509869:0.476332:0.519940:0.476332:0.519940:0.459612:0.509869:0.459612:0.000000
73:@0.464610:0.499782:0.502233:0.499782:0.502233:0.483062:0.464610:0.483062:0.000000:0.000000
2:@0.549865:0.476332:0.559936:0.476332:0.559936:0.459612:0.549865:0.459612:0.000000
7:@0.581771:0.476332:0.591842:0.476332:0.591842:0.459612:0.581771:0.459612:0.000000
3:@0.624965:0.476332:0.635037:0.476332:0.635037:0.459612:0.624965:0.459612:0.000000
4:@0.591615:0.499782:0.601686:0.499782:0.601686:0.483062:0.591615:0.483062:0.000000
7:@0.678500:0.479944:0.688571:0.479944:0.688571:0.463224:0.678500:0.463224:0.000000
3:@0.721715:0.479944:0.731786:0.479944:0.731786:0.463224:0.721715:0.463224:0.000000
2:@0.693916:0.499782:0.703987:0.499782:0.703987:0.483062:0.693916:0.483062:0.000000
.:@0.735171:0.489073:0.738762:0.489073:0.738762:0.472353:0.735171:0.472353:0.000000
número:@0.367510:0.442626:0.403105:0.442626:0.403105:0.432952:0.367510:0.432952:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
irracional:@0.367283:0.450811:0.409252:0.450811:0.409252:0.441137:0.367283:0.441137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
número:@0.680362:0.511371:0.715956:0.511371:0.715956:0.501698:0.680362:0.501698:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
racional:@0.680362:0.519557:0.716901:0.519557:0.716901:0.509883:0.680362:0.509883:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.653750:0.420948:0.659586:0.420948:0.659586:0.411258:0.653750:0.411258:0.000000
2:@0.718659:0.420948:0.724496:0.420948:0.724496:0.411258:0.718659:0.411258:0.000000
b.:@0.322121:0.569497:0.335963:0.569497:0.335963:0.552828:0.322121:0.552828:0.000000:0.000000
 :@0.335962:0.569497:0.339680:0.569497:0.339680:0.552315:0.335962:0.552315:0.000000
c.:@0.322121:0.639518:0.333994:0.639518:0.333994:0.622848:0.322121:0.622848:0.000000:0.000000
 :@0.333992:0.639518:0.337710:0.639518:0.337710:0.622335:0.333992:0.622335:0.000000
d.:@0.322121:0.709537:0.336129:0.709537:0.336129:0.692868:0.322121:0.692868:0.000000:0.000000
 :@0.336127:0.709537:0.339846:0.709537:0.339846:0.692355:0.336127:0.692355:0.000000
e.:@0.322121:0.837715:0.334933:0.837715:0.334933:0.821045:0.322121:0.821045:0.000000:0.000000
 :@0.334931:0.837715:0.338649:0.837715:0.338649:0.820532:0.334931:0.820532:0.000000
 :@0.849250:0.837715:0.853281:0.837715:0.853281:0.821281:0.849250:0.821281:0.000000
Competencia :@0.078581:0.146231:0.177272:0.146231:0.177272:0.130825:0.078581:0.130825:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.078581:0.161360:0.167195:0.161360:0.167195:0.145954:0.078581:0.145954:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para racionalizar radicales :@0.085343:0.190284:0.257752:0.190284:0.257752:0.175344:0.085343:0.175344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del tipo :@0.085343:0.213545:0.140247:0.213545:0.140247:0.198605:0.085343:0.198605:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
con   > 0,   > 0,:@0.085343:0.238343:0.190147:0.238343:0.190147:0.223403:0.085343:0.223403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.114342:0.238343:0.122759:0.238343:0.122759:0.223428:0.114342:0.223428:0.000000
c:@0.154805:0.238343:0.161766:0.238343:0.161766:0.223428:0.154805:0.223428:0.000000
multiplica el numerador :@0.085343:0.260620:0.249301:0.260620:0.249301:0.245680:0.085343:0.245680:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y el denominador :@0.085343:0.275749:0.207165:0.275749:0.207165:0.260809:0.085343:0.260809:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por la conjugada del :@0.085343:0.290878:0.226192:0.290878:0.226192:0.275938:0.085343:0.275938:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
denominador. :@0.085343:0.306007:0.182966:0.306007:0.182966:0.291067:0.085343:0.291067:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Así::@0.085343:0.328284:0.107649:0.328284:0.107649:0.313344:0.085343:0.313344:0.000000:0.000000:0.000000:0.000000
, la conjugada :@0.152279:0.350559:0.248532:0.350559:0.248532:0.335619:0.152279:0.335619:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es::@0.085343:0.365688:0.102612:0.365688:0.102612:0.350748:0.085343:0.350748:0.000000:0.000000:0.000000
. :@0.169547:0.365688:0.176123:0.365688:0.176123:0.350748:0.169547:0.350748:0.000000:0.000000
Y la conjugada de:@0.085343:0.387964:0.204321:0.387964:0.204321:0.373024:0.085343:0.373024:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es::@0.152279:0.410240:0.169548:0.410240:0.169548:0.395300:0.152279:0.395300:0.000000:0.000000:0.000000
 :@0.239829:0.410240:0.243494:0.410240:0.243494:0.395300:0.239829:0.395300:0.000000
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