Resolver sqrt{{8/3-1/2-[(1+1/3)^2:4/3+frac{1}{5}]*frac{5}{46}+(2-frac{1}{4})}:frac{3}{5}}

$$\sqrt { \{ \frac { 8 } { 3 } - \frac { 1 } { 2 } - [ ( 1 + \frac { 1 } { 3 } ) ^ { 2 } : \frac { 4 } { 3 } + \frac { 1 } { 5 } ] \times \frac { 5 } { 46 } + ( 2 - \frac { 1 } { 4 } ) \} : \frac { 3 } { 5 } }$$

Calcular

$$\frac{5}{2}=2.5$$

Pasos da solución

Resta \frac{1}{2} de \frac{8}{3} para obter \frac{13}{6}.

$$\sqrt{\frac{\frac{13}{6}-\left(\frac{\left(1+\frac{1}{3}\right)^{2}}{\frac{4}{3}}+\frac{1}{5}\right)\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Suma 1 e \frac{1}{3} para obter \frac{4}{3}.

$$\sqrt{\frac{\frac{13}{6}-\left(\frac{\left(\frac{4}{3}\right)^{2}}{\frac{4}{3}}+\frac{1}{5}\right)\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Calcula \frac{4}{3} á potencia de 2 e obtén \frac{16}{9}.

$$\sqrt{\frac{\frac{13}{6}-\left(\frac{\frac{16}{9}}{\frac{4}{3}}+\frac{1}{5}\right)\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Divide \frac{16}{9} entre \frac{4}{3} mediante a multiplicación de \frac{16}{9} polo recíproco de \frac{4}{3}.

$$\sqrt{\frac{\frac{13}{6}-\left(\frac{16}{9}\times \frac{3}{4}+\frac{1}{5}\right)\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Multiplica \frac{16}{9} e \frac{3}{4} para obter \frac{4}{3}.

$$\sqrt{\frac{\frac{13}{6}-\left(\frac{4}{3}+\frac{1}{5}\right)\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Suma \frac{4}{3} e \frac{1}{5} para obter \frac{23}{15}.

$$\sqrt{\frac{\frac{13}{6}-\frac{23}{15}\times \frac{5}{46}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Multiplica \frac{23}{15} e \frac{5}{46} para obter \frac{1}{6}.

$$\sqrt{\frac{\frac{13}{6}-\frac{1}{6}+2-\frac{1}{4}}{\frac{3}{5}}}$$

Resta \frac{1}{6} de \frac{13}{6} para obter 2.

$$\sqrt{\frac{2+2-\frac{1}{4}}{\frac{3}{5}}}$$

Suma 2 e 2 para obter 4.

$$\sqrt{\frac{4-\frac{1}{4}}{\frac{3}{5}}}$$

Resta \frac{1}{4} de 4 para obter \frac{15}{4}.

$$\sqrt{\frac{\frac{15}{4}}{\frac{3}{5}}}$$

Divide \frac{15}{4} entre \frac{3}{5} mediante a multiplicación de \frac{15}{4} polo recíproco de \frac{3}{5}.

$$\sqrt{\frac{15}{4}\times \frac{5}{3}}$$

Multiplica \frac{15}{4} e \frac{5}{3} para obter \frac{25}{4}.

$$\sqrt{\frac{25}{4}}$$

Reescribe a raíz cadrada da división \frac{25}{4} como a división de raíces cadradas \frac{\sqrt{25}}{\sqrt{4}}. Obtén a raíz cadrada do numerador e o denominador.

$$\frac{5}{2}$$

Factorizar

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$