Resolver sqrt{(11/4*8/11)^2:[(23/12-3/2):frac{5}{4}]^2}-sqrt{10+[(frac{1}{2})^2:frac{1}{2}+frac{12}{13}*(frac{5}{4}-frac{1}{6})]:frac{8}{3}}

$$\sqrt { ( \frac { 11 } { 4 } \times \frac { 8 } { 11 } ) ^ { 2 } : [ ( \frac { 23 } { 12 } - \frac { 3 } { 2 } ) : \frac { 5 } { 4 } ] ^ { 2 } } - \sqrt { 10 + [ ( \frac { 1 } { 2 } ) ^ { 2 } : \frac { 1 } { 2 } + \frac { 12 } { 13 } \times ( \frac { 5 } { 4 } - \frac { 1 } { 6 } ) ] : \frac { 8 } { 3 } }$$

Calcular

$$\frac{11}{4}=2.75$$

Pasos da solución

Para dividir potencias da mesma base, resta o expoñente do denominador do expoñente do numerador. Resta 1 de 2 para obter 1.

$$\sqrt{\frac{\left(\frac{11}{4}\times \frac{8}{11}\right)^{2}}{\left(\frac{\frac{23}{12}-\frac{3}{2}}{\frac{5}{4}}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Multiplica \frac{11}{4} e \frac{8}{11} para obter 2.

$$\sqrt{\frac{2^{2}}{\left(\frac{\frac{23}{12}-\frac{3}{2}}{\frac{5}{4}}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Calcula 2 á potencia de 2 e obtén 4.

$$\sqrt{\frac{4}{\left(\frac{\frac{23}{12}-\frac{3}{2}}{\frac{5}{4}}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Resta \frac{3}{2} de \frac{23}{12} para obter \frac{5}{12}.

$$\sqrt{\frac{4}{\left(\frac{\frac{5}{12}}{\frac{5}{4}}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Divide \frac{5}{12} entre \frac{5}{4} mediante a multiplicación de \frac{5}{12} polo recíproco de \frac{5}{4}.

$$\sqrt{\frac{4}{\left(\frac{5}{12}\times \frac{4}{5}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Multiplica \frac{5}{12} e \frac{4}{5} para obter \frac{1}{3}.

$$\sqrt{\frac{4}{\left(\frac{1}{3}\right)^{2}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Calcula \frac{1}{3} á potencia de 2 e obtén \frac{1}{9}.

$$\sqrt{\frac{4}{\frac{1}{9}}}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Divide 4 entre \frac{1}{9} mediante a multiplicación de 4 polo recíproco de \frac{1}{9}.

$$\sqrt{4\times 9}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Multiplica 4 e 9 para obter 36.

$$\sqrt{36}-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Calcular a raíz cadrada de 36 e obter 6.

$$6-\sqrt{10+\frac{\left(\frac{1}{2}\right)^{1}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Calcula \frac{1}{2} á potencia de 1 e obtén \frac{1}{2}.

$$6-\sqrt{10+\frac{\frac{1}{2}+\frac{12}{13}\left(\frac{5}{4}-\frac{1}{6}\right)}{\frac{8}{3}}}$$

Resta \frac{1}{6} de \frac{5}{4} para obter \frac{13}{12}.

$$6-\sqrt{10+\frac{\frac{1}{2}+\frac{12}{13}\times \frac{13}{12}}{\frac{8}{3}}}$$

Multiplica \frac{12}{13} e \frac{13}{12} para obter 1.

$$6-\sqrt{10+\frac{\frac{1}{2}+1}{\frac{8}{3}}}$$

Suma \frac{1}{2} e 1 para obter \frac{3}{2}.

$$6-\sqrt{10+\frac{\frac{3}{2}}{\frac{8}{3}}}$$

Divide \frac{3}{2} entre \frac{8}{3} mediante a multiplicación de \frac{3}{2} polo recíproco de \frac{8}{3}.

$$6-\sqrt{10+\frac{3}{2}\times \frac{3}{8}}$$

Multiplica \frac{3}{2} e \frac{3}{8} para obter \frac{9}{16}.

$$6-\sqrt{10+\frac{9}{16}}$$

Suma 10 e \frac{9}{16} para obter \frac{169}{16}.

$$6-\sqrt{\frac{169}{16}}$$

Reescribe a raíz cadrada da división \frac{169}{16} como a división de raíces cadradas \frac{\sqrt{169}}{\sqrt{16}}. Obtén a raíz cadrada do numerador e o denominador.

$$6-\frac{13}{4}$$

Resta \frac{13}{4} de 6 para obter \frac{11}{4}.

$$\frac{11}{4}$$

Factorizar

$$\frac{11}{2 ^ {2}} = 2\frac{3}{4} = 2.75$$