Solucionar sqrt{(left(0747-0500right)^2+left(0747-0440right)^2+left(0747-0460right)^2+left(0747-0640right)^2+{left(0747-0800right)}^2+{left(0747-0850right)}^2+{left(0747-1right)}^2+{left(0747-13right)}^2)div(8(8-1))}

$$\sqrt{ ( { \left(0747-0500 \right) }^{ 2 } + { \left(0747-0440 \right) }^{ 2 } + { \left(0747-0460 \right) }^{ 2 } + { \left(0747-0640 \right) }^{ 2 } + { \left(0747-0800 \right) }^{ 2 } + { \left(0747-0850 \right) }^{ 2 } + { \left(0747-1 \right) }^{ 2 } + { \left(0747-13 \right) }^{ 2 } ) \div (8(8-1)) }$$

Calcular

$$\frac{\sqrt{595}}{14}\approx 1,742330131$$

Pasos de la solución

Multiplica 0 y 747 para obtener 0.

$$\sqrt{\frac{\left(0-0\times 500\right)^{2}+\left(0\times 747-0\times 440\right)^{2}+\left(0\times 747-0\times 460\right)^{2}+\left(0\times 747-0\times 640\right)^{2}+\left(0\times 747-0\times 800\right)^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Multiplica 0 y 500 para obtener 0.

$$\sqrt{\frac{\left(0-0\right)^{2}+\left(0\times 747-0\times 440\right)^{2}+\left(0\times 747-0\times 460\right)^{2}+\left(0\times 747-0\times 640\right)^{2}+\left(0\times 747-0\times 800\right)^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Al restar 0 de su mismo valor, da como resultado 0.

$$\sqrt{\frac{0^{2}+\left(0\times 747-0\times 440\right)^{2}+\left(0\times 747-0\times 460\right)^{2}+\left(0\times 747-0\times 640\right)^{2}+\left(0\times 747-0\times 800\right)^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Calcula 0 a la potencia de 2 y obtiene 0.

$$\sqrt{\frac{0+\left(0\times 747-0\times 440\right)^{2}+\left(0\times 747-0\times 460\right)^{2}+\left(0\times 747-0\times 640\right)^{2}+\left(0\times 747-0\times 800\right)^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Multiplica 0 y 747 para obtener 0.

$$\sqrt{\frac{0+\left(0-0\times 440\right)^{2}+\left(0\times 747-0\times 460\right)^{2}+\left(0\times 747-0\times 640\right)^{2}+\left(0\times 747-0\times 800\right)^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Multiplica 0 y 440 para obtener 0.

$$\sqrt{\frac{0+\left(0-0\right)^{2}+\left(0\times 747-0\times 460\right)^{2}+\left(0\times 747-0\times 640\right)^{2}+\left(0\times 747-0\times 800\right)^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Al restar 0 de su mismo valor, da como resultado 0.

$$\sqrt{\frac{0+0^{2}+\left(0\times 747-0\times 460\right)^{2}+\left(0\times 747-0\times 640\right)^{2}+\left(0\times 747-0\times 800\right)^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Calcula 0 a la potencia de 2 y obtiene 0.

$$\sqrt{\frac{0+0+\left(0\times 747-0\times 460\right)^{2}+\left(0\times 747-0\times 640\right)^{2}+\left(0\times 747-0\times 800\right)^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Suma 0 y 0 para obtener 0.

$$\sqrt{\frac{\left(0\times 747-0\times 460\right)^{2}+\left(0\times 747-0\times 640\right)^{2}+\left(0\times 747-0\times 800\right)^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Multiplica 0 y 747 para obtener 0.

$$\sqrt{\frac{\left(0-0\times 460\right)^{2}+\left(0\times 747-0\times 640\right)^{2}+\left(0\times 747-0\times 800\right)^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Multiplica 0 y 460 para obtener 0.

$$\sqrt{\frac{\left(0-0\right)^{2}+\left(0\times 747-0\times 640\right)^{2}+\left(0\times 747-0\times 800\right)^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Al restar 0 de su mismo valor, da como resultado 0.

$$\sqrt{\frac{0^{2}+\left(0\times 747-0\times 640\right)^{2}+\left(0\times 747-0\times 800\right)^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Calcula 0 a la potencia de 2 y obtiene 0.

$$\sqrt{\frac{0+\left(0\times 747-0\times 640\right)^{2}+\left(0\times 747-0\times 800\right)^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Multiplica 0 y 747 para obtener 0.

$$\sqrt{\frac{0+\left(0-0\times 640\right)^{2}+\left(0\times 747-0\times 800\right)^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Multiplica 0 y 640 para obtener 0.

$$\sqrt{\frac{0+\left(0-0\right)^{2}+\left(0\times 747-0\times 800\right)^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Al restar 0 de su mismo valor, da como resultado 0.

$$\sqrt{\frac{0+0^{2}+\left(0\times 747-0\times 800\right)^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Calcula 0 a la potencia de 2 y obtiene 0.

$$\sqrt{\frac{0+0+\left(0\times 747-0\times 800\right)^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Suma 0 y 0 para obtener 0.

$$\sqrt{\frac{\left(0\times 747-0\times 800\right)^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Multiplica 0 y 747 para obtener 0.

$$\sqrt{\frac{\left(0-0\times 800\right)^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Multiplica 0 y 800 para obtener 0.

$$\sqrt{\frac{\left(0-0\right)^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Al restar 0 de su mismo valor, da como resultado 0.

$$\sqrt{\frac{0^{2}+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Calcula 0 a la potencia de 2 y obtiene 0.

$$\sqrt{\frac{0+\left(0\times 747-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Multiplica 0 y 747 para obtener 0.

$$\sqrt{\frac{0+\left(0-0\times 850\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Multiplica 0 y 850 para obtener 0.

$$\sqrt{\frac{0+\left(0-0\right)^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Al restar 0 de su mismo valor, da como resultado 0.

$$\sqrt{\frac{0+0^{2}+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Calcula 0 a la potencia de 2 y obtiene 0.

$$\sqrt{\frac{0+0+\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Suma 0 y 0 para obtener 0.

$$\sqrt{\frac{\left(0\times 747-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Multiplica 0 y 747 para obtener 0.

$$\sqrt{\frac{\left(0-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Resta 1 de 0 para obtener -1.

$$\sqrt{\frac{\left(-1\right)^{2}+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Calcula -1 a la potencia de 2 y obtiene 1.

$$\sqrt{\frac{1+\left(0\times 747-13\right)^{2}}{8\left(8-1\right)}}$$

Multiplica 0 y 747 para obtener 0.

$$\sqrt{\frac{1+\left(0-13\right)^{2}}{8\left(8-1\right)}}$$

Resta 13 de 0 para obtener -13.

$$\sqrt{\frac{1+\left(-13\right)^{2}}{8\left(8-1\right)}}$$

Calcula -13 a la potencia de 2 y obtiene 169.

$$\sqrt{\frac{1+169}{8\left(8-1\right)}}$$

Suma 1 y 169 para obtener 170.

$$\sqrt{\frac{170}{8\left(8-1\right)}}$$

Resta 1 de 8 para obtener 7.

$$\sqrt{\frac{170}{8\times 7}}$$

Multiplica 8 y 7 para obtener 56.

$$\sqrt{\frac{170}{56}}$$

Reduzca la fracción \frac{170}{56} a su mínima expresión extrayendo y anulando 2.

$$\sqrt{\frac{85}{28}}$$

Vuelva a escribir la raíz cuadrada de la división \sqrt{\frac{85}{28}} como la división de las raíces cuadradas \frac{\sqrt{85}}{\sqrt{28}}.

$$\frac{\sqrt{85}}{\sqrt{28}}$$

Factorice 28=2^{2}\times 7. Vuelve a escribir la raíz cuadrada del producto \sqrt{2^{2}\times 7} como el producto de las raíces cuadradas \sqrt{2^{2}}\sqrt{7}. Toma la raíz cuadrada de 2^{2}.

$$\frac{\sqrt{85}}{2\sqrt{7}}$$

Racionaliza el denominador de \frac{\sqrt{85}}{2\sqrt{7}} multiplicando el numerador y el denominador \sqrt{7}.

$$\frac{\sqrt{85}\sqrt{7}}{2\left(\sqrt{7}\right)^{2}}$$

El cuadrado de \sqrt{7} es 7.

$$\frac{\sqrt{85}\sqrt{7}}{2\times 7}$$

Para multiplicar \sqrt{85} y \sqrt{7}, multiplique los números bajo la raíz cuadrada.

$$\frac{\sqrt{595}}{2\times 7}$$

Multiplica 2 y 7 para obtener 14.

$$\frac{\sqrt{595}}{14}$$