Resolver sqrt{{[(2/3+1/2)-1/6]^2}^3+1-(2/3+frac{7}{6}+frac{2}{12})+[15*(frac{1}{3}+frac{1}{5})]^2}

$$\sqrt { \{ [ ( \frac { 2 } { 3 } + \frac { 1 } { 2 } ) - \frac { 1 } { 6 } ] ^ { 2 } \} ^ { 3 } + 1 - ( \frac { 2 } { 3 } + \frac { 7 } { 6 } + \frac { 2 } { 12 } ) + [ 15 \times ( \frac { 1 } { 3 } + \frac { 1 } { 5 } ) ] ^ { 2 } }$$

Calcular

$$8$$

Pasos da solución

Para elevar unha potencia a outra potencia, multiplica os expoñentes. Multiplica 2 e 3 para obter 6.

$$\sqrt{\left(\frac{2}{3}+\frac{1}{2}-\frac{1}{6}\right)^{6}+1-\left(\frac{2}{3}+\frac{7}{6}+\frac{2}{12}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

Suma \frac{2}{3} e \frac{1}{2} para obter \frac{7}{6}.

$$\sqrt{\left(\frac{7}{6}-\frac{1}{6}\right)^{6}+1-\left(\frac{2}{3}+\frac{7}{6}+\frac{2}{12}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

Resta \frac{1}{6} de \frac{7}{6} para obter 1.

$$\sqrt{1^{6}+1-\left(\frac{2}{3}+\frac{7}{6}+\frac{2}{12}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

Calcula 1 á potencia de 6 e obtén 1.

$$\sqrt{1+1-\left(\frac{2}{3}+\frac{7}{6}+\frac{2}{12}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

Suma 1 e 1 para obter 2.

$$\sqrt{2-\left(\frac{2}{3}+\frac{7}{6}+\frac{2}{12}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

Suma \frac{2}{3} e \frac{7}{6} para obter \frac{11}{6}.

$$\sqrt{2-\left(\frac{11}{6}+\frac{2}{12}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

Reduce a fracción \frac{2}{12} a termos máis baixos extraendo e cancelando 2.

$$\sqrt{2-\left(\frac{11}{6}+\frac{1}{6}\right)+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

Suma \frac{11}{6} e \frac{1}{6} para obter 2.

$$\sqrt{2-2+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

Resta 2 de 2 para obter 0.

$$\sqrt{0+\left(15\left(\frac{1}{3}+\frac{1}{5}\right)\right)^{2}}$$

Suma \frac{1}{3} e \frac{1}{5} para obter \frac{8}{15}.

$$\sqrt{0+\left(15\times \frac{8}{15}\right)^{2}}$$

Multiplica 15 e \frac{8}{15} para obter 8.

$$\sqrt{0+8^{2}}$$

Calcula 8 á potencia de 2 e obtén 64.

$$\sqrt{0+64}$$

Suma 0 e 64 para obter 64.

$$\sqrt{64}$$

Calcular a raíz cadrada de 64 e obter 8.

$$8$$

Factorizar

$$2^{3}$$