Solucionar (54002341048623*(4+8))/(sqrt{88247711001123870*4287)+84/81}

$$\frac { ( 54002341048623 \cdot ( 4 + 8 ) ) } { ( \sqrt { 88247711001123870 \cdot 4287 } ) + \frac { 84 } { 81 } }$$

Calcular

$$\frac{708618719240031006\sqrt{42035326340202003410}}{137896888059032672186113}-\frac{34993516999507704}{19699555437004667455159}\approx 33316,959958538$$

Pasos de la solución

Suma 4 y 8 para obtener 12.

$$\frac{54002341048623\times 12}{\sqrt{88247711001123870\times 4287}+\frac{84}{81}}$$

Multiplica 54002341048623 y 12 para obtener 648028092583476.

$$\frac{648028092583476}{\sqrt{88247711001123870\times 4287}+\frac{84}{81}}$$

Multiplica 88247711001123870 y 4287 para obtener 378317937061818030690.

$$\frac{648028092583476}{\sqrt{378317937061818030690}+\frac{84}{81}}$$

Factorice 378317937061818030690=3^{2}\times 42035326340202003410. Vuelve a escribir la raíz cuadrada del producto \sqrt{3^{2}\times 42035326340202003410} como el producto de las raíces cuadradas \sqrt{3^{2}}\sqrt{42035326340202003410}. Toma la raíz cuadrada de 3^{2}.

$$\frac{648028092583476}{3\sqrt{42035326340202003410}+\frac{84}{81}}$$

Reduzca la fracción \frac{84}{81} a su mínima expresión extrayendo y anulando 3.

$$\frac{648028092583476}{3\sqrt{42035326340202003410}+\frac{28}{27}}$$

Racionaliza el denominador de \frac{648028092583476}{3\sqrt{42035326340202003410}+\frac{28}{27}} multiplicando el numerador y el denominador 3\sqrt{42035326340202003410}-\frac{28}{27}.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{\left(3\sqrt{42035326340202003410}+\frac{28}{27}\right)\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}$$

Piense en \left(3\sqrt{42035326340202003410}+\frac{28}{27}\right)\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right). La multiplicación se puede transformar en la diferencia de cuadrados mediante la regla: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{\left(3\sqrt{42035326340202003410}\right)^{2}-\left(\frac{28}{27}\right)^{2}}$$

Expande \left(3\sqrt{42035326340202003410}\right)^{2}.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{3^{2}\left(\sqrt{42035326340202003410}\right)^{2}-\left(\frac{28}{27}\right)^{2}}$$

Calcula 3 a la potencia de 2 y obtiene 9.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{9\left(\sqrt{42035326340202003410}\right)^{2}-\left(\frac{28}{27}\right)^{2}}$$

El cuadrado de \sqrt{42035326340202003410} es 42035326340202003410.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{9\times 42035326340202003410-\left(\frac{28}{27}\right)^{2}}$$

Multiplica 9 y 42035326340202003410 para obtener 378317937061818030690.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{378317937061818030690-\left(\frac{28}{27}\right)^{2}}$$

Calcula \frac{28}{27} a la potencia de 2 y obtiene \frac{784}{729}.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{378317937061818030690-\frac{784}{729}}$$

Convertir 378317937061818030690 a la fracción \frac{275793776118065344373010}{729}.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{\frac{275793776118065344373010}{729}-\frac{784}{729}}$$

Como \frac{275793776118065344373010}{729} y \frac{784}{729} tienen el mismo denominador, reste sus numeradores para restarlos.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{\frac{275793776118065344373010-784}{729}}$$

Resta 784 de 275793776118065344373010 para obtener 275793776118065344372226.

$$\frac{648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)}{\frac{275793776118065344372226}{729}}$$

Divide 648028092583476\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right) entre \frac{275793776118065344372226}{729} para obtener \frac{236206239746677002}{137896888059032672186113}\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right).

$$\frac{236206239746677002}{137896888059032672186113}\left(3\sqrt{42035326340202003410}-\frac{28}{27}\right)$$

Usa la propiedad distributiva para multiplicar \frac{236206239746677002}{137896888059032672186113} por 3\sqrt{42035326340202003410}-\frac{28}{27}.

$$\frac{236206239746677002}{137896888059032672186113}\times 3\sqrt{42035326340202003410}+\frac{236206239746677002}{137896888059032672186113}\left(-\frac{28}{27}\right)$$

Expresa \frac{236206239746677002}{137896888059032672186113}\times 3 como una única fracción.

$$\frac{236206239746677002\times 3}{137896888059032672186113}\sqrt{42035326340202003410}+\frac{236206239746677002}{137896888059032672186113}\left(-\frac{28}{27}\right)$$

Multiplica 236206239746677002 y 3 para obtener 708618719240031006.

$$\frac{708618719240031006}{137896888059032672186113}\sqrt{42035326340202003410}+\frac{236206239746677002}{137896888059032672186113}\left(-\frac{28}{27}\right)$$

Multiplica \frac{236206239746677002}{137896888059032672186113} por -\frac{28}{27} (para hacerlo, multiplica el numerador por el numerador y el denominador por el denominador).

$$\frac{708618719240031006}{137896888059032672186113}\sqrt{42035326340202003410}+\frac{236206239746677002\left(-28\right)}{137896888059032672186113\times 27}$$

Realiza las multiplicaciones en la fracción \frac{236206239746677002\left(-28\right)}{137896888059032672186113\times 27}.

$$\frac{708618719240031006}{137896888059032672186113}\sqrt{42035326340202003410}+\frac{-6613774712906956056}{3723215977593882149025051}$$

Reduzca la fracción \frac{-6613774712906956056}{3723215977593882149025051} a su mínima expresión extrayendo y anulando 189.

$$\frac{708618719240031006}{137896888059032672186113}\sqrt{42035326340202003410}-\frac{34993516999507704}{19699555437004667455159}$$

Factorizar

$$\frac{8748379249876926 {(81 \sqrt{42035326340202003410} - 28)}}{137896888059032672186113} = 33316\frac{1,3237529501491374 \times 10^{23}}{1,3789688805903266 \times 10^{23}} = 33316,9599585377$$