Números Reales
Los números reales están formado por el conjunto de los números
fraccionarios, los que se pueden poner en forma de fracción junto con
los irracionales que son los que no admiten expresión fraccionaria.
Operaciones con fracciones
Introducción a los números reales
Números racionales:
Son
todos aquellos que se pueden poner en forma de fracción. Cualquier
número decimal con un número finito de cifras o con infinitas cifras
periódicas se puede poner en forma de fracción.
Halla una expresión decimal para las siguientes fracciones:
Encuentra las fracciones equivalentes para los siguientes números
decimales:
Dado los siguientes números :
Di cuáles son:
a) Reales
b) Irracionales
c) Racionales
d) Naturales
e) Enteros
Escribe las aproximaciones por defecto de los números:
para que el error cometido sea menor de:
Una décima
Una milésima
Escribe las aproximaciones por exceso de décima,
centésima y milésima de los números anteriores.
Recta Real
Podemos
dibujar una recta de forma que a cada número real le corresponda un
punto y al revés que a cada punto le corresponda un numero.
Representación de los números reales: Intervalos
Dado
un número cualquiera, podemos representar todos los números
reales
mayores que ese número por un intervalo abierto por los dos lados, por
medio de desigualdades o dibujándolos en la recta.
De
la misma forma se pueden representar los números comprendidos entre – 3
y 1, es decir los números más grandes que -3 y más pequeños que 1
Si en vez de estrictamente menor fuera menor o igual los extremos
pertenecen al intervalo y éste se llama cerrado.
También puede haber intervalos abiertos por la derecha y cerrados por
la izquierda y al revés.
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Cuando uno de los extremos es infinito el intervalo siempre es abierto
![Ir Inicio](../imagenes/boton_arriba.gif)
Potencias con exponente fraccionario
Una raíz no es más que una potencia con exponente fraccionario escrita
de otra forma, por tanto tienen las misma propiedades que las potencias.
1 Calcula:
2 Halla el valor de x
Simplificar potencias:
3 Simplifica los siguientes radicales:
4 Escribe como potencias de exponente racional:
5) Halla el valor de las siguientes potencias:
Introducción de factores dentro de una raíz.
En
algunos casos cuando tenemos una raíz multiplicada por uno o varios
factores, nos puede interesar introducirlos dentro de la raíz. Para
ello elevamos los factores que queremos introducir al índice de la raíz
y lo ponemos dentro.
Ejemplos:
I)
II)
Extracción de factores en un radical
Es
el proceso inverso al anterior, para poder sacar factores de la raíz
estos tienen que estar elevado a un exponente mayor que el índice y se
descomponen en producto de factores con exponentes divisibles por el
índice. Para sacarlos se divide el exponente por el índice.
Multiplicación y divison de radicales
Si
tienen el mismo índice se multiplican o dividen los radicandos y se
queda el mismo índice. Del resultado se extraen fuera de la raíz los
factores que se puedan.
Si tienen distinto índice se transforman primero en radicales semejantes con índice común.
División de radicales:
Suma de radicales: No se pueden sumar lo único que podemos hacer es agrupar los que son iguales.
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qdnK9+TMT1YVLjvqfUYppa/he5x+l48YY7L6r0ulyu5jZ3lS5wvS1vdpqEvPML9Tz97Xm7N3wl69z6zl9n649njDn2bKz5YTy5fYkFnLsYE89An2abnev3gOAADgqCw7f6wc91Jqlerpq//msq57WIG4x3DPFh9KrloFcJPs/7WjlZr7PJyndNlR78tZu3fBANAtvLl6Ossqr6W6+Gk9VOfL0db/1ePOHyXkXOmr3pelvaekkuVLbChLbCAXfYL6eQ4AACCHXDt/nL07h4fbig2rVNbu0emrAO6Q/T/wEMheRcuOel/O8L3O3adHCOF7ZYcsbqT0wP6n9VCdL0pbzxk+bjvU+7K095RUsnyJDWWJDZxAn6AengMAADjscPLH8KBZMvnDg+zNXPTQMi5HTa6OWXhA9hDIphrKjnp/zHDtS9dv0Pf+zii7WcuQOr9PDfGafuSefFHvj9PeU9JV5UtsOE5soDR9gut5DgAAIJc/GV5j8SHzaEd75QG2qQ48s55hvuw8YoyPnA9pd8j+X9ies/qHwBucRdzcgMFUZWVHvT8gpfS1sn3udwjh8iMR1PkmLNXDM99LnZ9RWbxetZH8Xeo9i8eXGr/rozbajhLU+4NaaO9p14XlS2w4qIXY4FmgbvoE9WrpOQAAgPrFlPb3+1fOIgwhQyd16TzKK878nntAcvb4fqXLzuS97njmZ/Wf4+RBhZKq/66X1FZ21PvjVs5pDuHiz6nO77dxX0PIeE1nliF1/n21xes1G/e1dVV+50etxefczzPqfR41t/e074ryJTbkUXNs8CzQBn2C+rT0HAAAQBuOHvuyOlFx8LXPfl1OtLFt6SPXtqUzr9NU+Vl4CPzyEMiWGsuOep/F2mfJ9h1Sl1Zjvjr/nhrj9YY7x5k7f7ZTqPfZaO8p6fTyJTZkIzbQDPV+W4PPAQAANKBY8kem7fs8uN7b6sBFpvdo9szPlYfAVj5DK9e5Zm2wolqVlx31/oA3PsuV7eYdvudL6nxFg3slyo86v6LyeD1rKK/VXt9BtdTF0xTaol+9P6jy9p7GXVi+xIaDKo8Nd/ium3z+z0Wf4FwtPgcAANCGo8e+LP1yjiNflrYHvKQj7NiXMta2LT36/c6UoaYeombKXFPXz3VqLzvq/TFvbKl8u8/cg7O2YN46YqZE30adX1Z7vL7StNzod++30W6UOuJBvT9Ie09JV5UvseE4sYEj9Anq4TkAAIBSdu/8USgjfGzpwUBHuBMZyliT2f8hzH52D4G8pfWy03O9/0DNK/7gIz3X+dbjNXnEGB8xxu8YYxp+vu++bX/P9f5D2ntKqq58iQ1vq+7ekYc+wS5N1nvPAQAAlHT02JclpTqsOsI3s7GqYPdD7vCA3ORD8mRVxDOlFD0E8o5Wyo56D31R5//VSrymrNFq1XE5foQQmp/sUe+BOWIDzNMn+Fyr9d5zAAAApRVJ/sjUaW2uA89ui+XlwCqAX+WnxNaVJcw8BDZx3VyvwbJz23o/s2IrnbBb1pj2s013H/C7bZ3/VIPxmnLW4vUdYvmt6732npJuXr7EhrLEhjbpE3yumnr/Ls8BAACc4c+B3116+Dg8ebGS1V7TxEhN19K0lNLXyrmjHz/kzmT/N3Gvcj8Evh6gPUzeX4tl5671fubM4ZdHjPFbfWSPGOOj9dVgd63zn2oxXlPUrSd67lzvtfd/nTyhfYoa7t3dy5fYALP0CT5QU71/l+cAAADOciT5o6TZjv9VEx+tb7HYiGdYuO87BklazP4fP7jmyv5XbjvQeNm5Y71fmwQx6MuiNwZEz+gDlX6PO9b5tzUer7kv9X6f7tv7lTaraZXcux7Kl9gA9dEnKMRzAAAAZypy7EsGcx3Y1YeQ0daaJTq/OtSF5XpQazT7f7w6KMtD4GgVXvWfn/1aLzt3q/dvrn7VntCtu9X5T7Qer7nEKfe1dHL9Heu99v72Lr13vZQvsQE+ok8wUlO9f4fnAAAAzlYi+eOqjue08097lsrO44Oknhaz/7M+BNKHG5Wd7ur9CQwAtauHe9ddnb9RvOZcWeLBxmTkWTGnu3p/kqvbjKvfvxRl668rdxwTG465a93smT7B5N+O/6Pmeu85AACAK2RP/jiaKb7yMLL1uo8c7/8BD9T5rX2nmw+Bsv/pxc3KTlf1HjZcWn5PiiVd1fmbxWvymyu/zxDC11XHXRbSVb3vRUrpK6UUb/ijfJ1HbID/6BPcrN57DgAA4CpHkj9O7WCvPeyMssNPu6abPXxVYfhOj6wCaCb7f5D7vM/Z1878utThNmWnw3qf43vd+k7U+0at9C1y7my29FrqfBm3ideUNZp4Pm2S56z602G9D0F7T1m3KF9iw26X3zvK0idY1VK99xwAAMAlShz7ctRcR/+tXT8KcpzMeY6sAmgi+z+Enx1uHqHAQ+D4YVmS0v3ctOzcot6/cz/OGJxS75t31f1T5zO7abwmo3G5+GCr809dmvD15vs1Ve+195TUYfkSG/Jfx+XfBZ/TJ/jRVL1f4jkAAIArVZX8sXH+5JqzM551rgvZWgWw9HvTslNz9n/Jh8CBZKWbumvZ6aHeh2HL3qMv8kY7qX1q3FI5zjEIvPYaZw4c9lDn7xqvKeJVF7Lf0424ccUujreu9wPtPSXdrnyJDZ+p6d5RhD7BDeq95wAAAK72Z+8vppS+Yowp14WMOsef/p6M547EGL8XHp5ay/4f/3dOTXwPfK7nstNYvX+G3wmJz5Mn1ascAONj43L08gjHy/lSP6uqctNYnf9Hz/GaXV71/RFjfGRuMxZX+Nb23NRgvdfeU5LyNRAbPlPTvWMXfYLQZL3/4TkAAIAaxJT2528sJGx8nNk8JHCsdYgXX7N0RnWuz8hn1hKLUkpx8m9/3aPp39fijXKem3J6E72UnbvU+8nnyHZO8xvl4LQzoSlvoT4cuscLr3lZW3GXOj/WS7w+Qyv3PIfxZ831OVfK4qVl5k71XntPSb2VL7Hhrdet8t6Rlz7BX63V+xA8BwAAUI9Dx77k6GROOsdf4fPM5bOPfLGa4hyL93Mmc776zPcLHgK5ic7Kzl3q/biN+M54ZvPqVr0Ge29na7XbR5ZWnV3cp7lLnQ8hdBevyeunTGdcIbr0OlfXnzvVe+09JfVWvsSGbbXeO/LSJwjt1XvPAQAA1ORQ8sdg2ul+vPtwO3TmfxI/Pn1YHT0MnPmgW91Dxh1tTEYtbqFYY2LOhQ+Bymrjeis7d6n3Q3uUddB342g0K35uaOEs7MeeQeCV8nNpublLnQ+hv3hNXpN24xFjPNRurMSJy1eF36nea+8pqbfyJTasq/nekZc+wY9m6r3nAAAAanM4+WPodP8zObH2OzHGx+Th9eehY+H1Zl8jnLPrR65VGnxubRXA677I/l9w9YM8x3Rcdpqv9yEsDvruGrgz2NuvpT7WJwkga4kflbQTzdf5juM1GU0ne8KOycKZZ6yxWup8CDeo9y/ae0rqsHyJDTMauXdkpE/wVwv13nMAAAA1iiktHrH42QvNP1T8ehAdTVaMkzb+2bVjofP883Ayea9iD7tb10F5K2eAvu7BuMxVd282BmqKqvEMVN7Xc9lpvd6PLbQj42THrd8dJzpOVf3ZyWepjxVWdj5bKT+rv3eF1ut8z/G6pBbOdi9hpt14t81YKodVTgy2Xu+ntPeU1FP5Ehv++d1m7h356RPUX+89BwAAUKNsyR8hfJzxvPrQ8caD7uZrHDXXide5PtcHD1K1PsR6EGSXnstO6/V+ztaKvZk/u6zto04bfax3d2Crsuy0Xud7jtcl9Zr8EcJm8tac5iYGW6/3S7T3lNRD+RIbfjR37yhDn+CX6sq+5wAAAGqUNfnj50X/3eHj5a0s9Tde65RVqzOd+OoeNO7ug4Siah9kgc/cud4fHByqbscGzrezDFXdf7lznWe/npM/XvbW9xA+e966wt3rvfaeku5cvsSGVVXfO8rSJwghNFrvAQDgbEWSP+5iZutBDxoXeOMht+pJLeBzd6/3oxVcIWyvAjTIyz9WEm1DGK0EbKWe3L3O8znJH/95o81osr3ood5r7ynpruVLbPjR3L2jPH0CAABgi+SPBXb9qMcbqwAk5cDNqPfQF3WeKckf96feA3PEBuiPeg8AAPlI/lgwk/zhQeNCM7uwvEjKgZtS76Ev6jxjkj/6oN4Dc8QG6I96DwAAefzv6guo0WQbxRBCCBI/Lrf0/bsvcF/qPfRFnYf+qPfAHLEB+qPeAwBABnb+mOHIlzrNrAJwX+Dm1HvoizrPi50/+qHeA3PEBuiPeg8AAMfZ+WPedNcPDxp1mGb7y/6H+1PvoS/qPCGEn/736/7ri9+beg/MERugP+o9AAAcJPljYlhlOOZBoxKTSYCno3jg/tR76Is6z1hK6SulFJWDe1PvgTliA/RHvQcAgOMc+zIx2WLQ9oIAAAAAAAAAQNXs/DFi1w8AAAAAAAAAoDV2/hix6wcAAAAAAAAA0Bo7fwymu35I/AAAAAAAAAAAWiD5I4QQY3yEEB6jP5L4AQAAAAAAAAA0QfLHX+PEj2dK6XnZlQAAAAAAAAAAfKD75I/huJdX8sfTcS8AAAAAAAAAQEu6Tv6YHPci8QMAAAAAAAAAaE63yR9D4sf38J8SPwAAAAAAAACAJnWZ/DFJ/AghhOdV1wIAAAAAAAAAcMSfqy/gIj9HvYS/u35I/gAAAAAAAAAAmtRd8keM8Tv8Tf5w1AsAAAAAAAAA0Lyujn0ZjnuR+AEAAAAAAAAA3EZMKV19DQAAAAAAAAAA7NTVzh8AAAAAAAAAAHcj+QMAAAAAAAAAoGGSPwAAAAAAAAAAGib5AwAAAAAAAACgYZI/AAAAAAAAAAAaJvkDAAAAAAAAAKBhkj8AAAAAAAAAABom+QMAAAAAAAAAoGGSPwAAAAAAAAAAGib5AwAAAAAAAACgYZI/AAAAAAAAAAAaJvkDAAAAAAAAAKBhkj8AAAAAAAAAABom+QMAAAAAAAAA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)
6 Expresa en forma de potencias de exponente entero positivo.
7 Calcula y simplifica:
![](data:image/*;base64,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)
8 Calcula
![](potencias/pot_07.gif)
9-a Extrae factores fuera de la raíz
9-b
10
11 Introduce factores dentro de la raíz
![](reales/image001.gif)
12 Simplifica todo lo que puedas
![](reales/image002.gif)
13 Calcula:
14 Calculad:
15
16
17
18
19 Extrae fuera de la raíz
20 Calcula
21 Escribe con exponente fraccionario.
22 Racionaliza
23 Simplifica
24
Inecuaciones primer grado
Logaritmos
Desarrollo histórico.
Los
logaritmos aparecen en matemáticas con el único fin de reducir en un
grado las operaciones y facilitar el trabajo de los calculistas. Su
principal propiedad es:
Llamamos logaritmo de un número a en una base determinada b al número que hay que elevar la base para que nos de el número a
Calcula a partir de la definición de logaritmo:
Halla el valor de x:
![](logaritmos/logaritmo003.gif)
Ejercicios
1
Calcula:
2
3 Halla el valor de x
4
Sabiendo que :
![](logaritmos/image004.gif)
calcula:
5
Halla el valor de x
6
Halla el valor de x con ayuda de la calculadora
Ecuaciones exponenciales y logarítmicas
1
Halla el valor de x
2 Resuelve y comprueba el resultado:
3 Halla el valor de x
5 Resuelve y comprueba el resultado