Solucionar sqrt{{3/2*3/10+[9/5-frac{3/5*(2-frac{1}{3})^2]*frac{3}{2}}:(frac{3}{5}+2)}{frac{2}{3}*[frac{1}{6}+frac{2}{13}*(frac{1}{4}+3)]}}

$$\sqrt { \frac { \{ \frac { 3 } { 2 } \times \frac { 3 } { 10 } + [ \frac { 9 } { 5 } - \frac { 3 } { 5 } \times ( 2 - \frac { 1 } { 3 } ) ^ { 2 } ] \times \frac { 3 } { 2 } \} : ( \frac { 3 } { 5 } + 2 ) } { \frac { 2 } { 3 } \times [ \frac { 1 } { 6 } + \frac { 2 } { 13 } \times ( \frac { 1 } { 4 } + 3 ) ] } }$$

Calcular

$$\frac{3}{4}=0,75$$

Pasos de la solución

Multiplica \frac{3}{2} y \frac{3}{10} para obtener \frac{9}{20}.

$$\sqrt{\frac{\frac{\frac{9}{20}+\left(\frac{9}{5}-\frac{3}{5}\left(2-\frac{1}{3}\right)^{2}\right)\times \frac{3}{2}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Resta \frac{1}{3} de 2 para obtener \frac{5}{3}.

$$\sqrt{\frac{\frac{\frac{9}{20}+\left(\frac{9}{5}-\frac{3}{5}\times \left(\frac{5}{3}\right)^{2}\right)\times \frac{3}{2}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Calcula \frac{5}{3} a la potencia de 2 y obtiene \frac{25}{9}.

$$\sqrt{\frac{\frac{\frac{9}{20}+\left(\frac{9}{5}-\frac{3}{5}\times \frac{25}{9}\right)\times \frac{3}{2}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Multiplica \frac{3}{5} y \frac{25}{9} para obtener \frac{5}{3}.

$$\sqrt{\frac{\frac{\frac{9}{20}+\left(\frac{9}{5}-\frac{5}{3}\right)\times \frac{3}{2}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Resta \frac{5}{3} de \frac{9}{5} para obtener \frac{2}{15}.

$$\sqrt{\frac{\frac{\frac{9}{20}+\frac{2}{15}\times \frac{3}{2}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Multiplica \frac{2}{15} y \frac{3}{2} para obtener \frac{1}{5}.

$$\sqrt{\frac{\frac{\frac{9}{20}+\frac{1}{5}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Suma \frac{9}{20} y \frac{1}{5} para obtener \frac{13}{20}.

$$\sqrt{\frac{\frac{\frac{13}{20}}{\frac{3}{5}+2}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Suma \frac{3}{5} y 2 para obtener \frac{13}{5}.

$$\sqrt{\frac{\frac{\frac{13}{20}}{\frac{13}{5}}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Divide \frac{13}{20} por \frac{13}{5} al multiplicar \frac{13}{20} por el recíproco de \frac{13}{5}.

$$\sqrt{\frac{\frac{13}{20}\times \frac{5}{13}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Multiplica \frac{13}{20} y \frac{5}{13} para obtener \frac{1}{4}.

$$\sqrt{\frac{\frac{1}{4}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\left(\frac{1}{4}+3\right)\right)}}$$

Suma \frac{1}{4} y 3 para obtener \frac{13}{4}.

$$\sqrt{\frac{\frac{1}{4}}{\frac{2}{3}\left(\frac{1}{6}+\frac{2}{13}\times \frac{13}{4}\right)}}$$

Multiplica \frac{2}{13} y \frac{13}{4} para obtener \frac{1}{2}.

$$\sqrt{\frac{\frac{1}{4}}{\frac{2}{3}\left(\frac{1}{6}+\frac{1}{2}\right)}}$$

Suma \frac{1}{6} y \frac{1}{2} para obtener \frac{2}{3}.

$$\sqrt{\frac{\frac{1}{4}}{\frac{2}{3}\times \frac{2}{3}}}$$

Multiplica \frac{2}{3} y \frac{2}{3} para obtener \frac{4}{9}.

$$\sqrt{\frac{\frac{1}{4}}{\frac{4}{9}}}$$

Divide \frac{1}{4} por \frac{4}{9} al multiplicar \frac{1}{4} por el recíproco de \frac{4}{9}.

$$\sqrt{\frac{1}{4}\times \frac{9}{4}}$$

Multiplica \frac{1}{4} y \frac{9}{4} para obtener \frac{9}{16}.

$$\sqrt{\frac{9}{16}}$$

Vuelva a escribir la raíz cuadrada de la división \frac{9}{16} como la división de las raíces cuadradas \frac{\sqrt{9}}{\sqrt{16}}. Toma la raíz cuadrada del numerador y el denominador.

$$\frac{3}{4}$$

Factorizar

$$\frac{3}{2 ^ {2}} = 0,75$$