Resolver sqrt{frac{5(1-11)^{2}+(4-11)^2+(11-11)^2+(20-11)^2+(18-11)^2}{5-1}}

$$\sqrt { \frac { 5 ( 1 - 11 ) ^ { 2 } + ( 4 - 11 ) ^ { 2 } + ( 11 - 11 ) ^ { 2 } + ( 20 - 11 ) ^ { 2 } + ( 18 - 11 ) ^ { 2 } } { 5 - 1 } }$$

Calcular

$$\frac{\sqrt{679}}{2}\approx 13.028814221$$

Pasos da solución

Resta 11 de 1 para obter -10.

$$\sqrt{\frac{5\left(-10\right)^{2}+\left(4-11\right)^{2}+\left(11-11\right)^{2}+\left(20-11\right)^{2}+\left(18-11\right)^{2}}{5-1}}$$

Calcula -10 á potencia de 2 e obtén 100.

$$\sqrt{\frac{5\times 100+\left(4-11\right)^{2}+\left(11-11\right)^{2}+\left(20-11\right)^{2}+\left(18-11\right)^{2}}{5-1}}$$

Multiplica 5 e 100 para obter 500.

$$\sqrt{\frac{500+\left(4-11\right)^{2}+\left(11-11\right)^{2}+\left(20-11\right)^{2}+\left(18-11\right)^{2}}{5-1}}$$

Resta 11 de 4 para obter -7.

$$\sqrt{\frac{500+\left(-7\right)^{2}+\left(11-11\right)^{2}+\left(20-11\right)^{2}+\left(18-11\right)^{2}}{5-1}}$$

Calcula -7 á potencia de 2 e obtén 49.

$$\sqrt{\frac{500+49+\left(11-11\right)^{2}+\left(20-11\right)^{2}+\left(18-11\right)^{2}}{5-1}}$$

Suma 500 e 49 para obter 549.

$$\sqrt{\frac{549+\left(11-11\right)^{2}+\left(20-11\right)^{2}+\left(18-11\right)^{2}}{5-1}}$$

Resta 11 de 11 para obter 0.

$$\sqrt{\frac{549+0^{2}+\left(20-11\right)^{2}+\left(18-11\right)^{2}}{5-1}}$$

Calcula 0 á potencia de 2 e obtén 0.

$$\sqrt{\frac{549+0+\left(20-11\right)^{2}+\left(18-11\right)^{2}}{5-1}}$$

Suma 549 e 0 para obter 549.

$$\sqrt{\frac{549+\left(20-11\right)^{2}+\left(18-11\right)^{2}}{5-1}}$$

Resta 11 de 20 para obter 9.

$$\sqrt{\frac{549+9^{2}+\left(18-11\right)^{2}}{5-1}}$$

Calcula 9 á potencia de 2 e obtén 81.

$$\sqrt{\frac{549+81+\left(18-11\right)^{2}}{5-1}}$$

Suma 549 e 81 para obter 630.

$$\sqrt{\frac{630+\left(18-11\right)^{2}}{5-1}}$$

Resta 11 de 18 para obter 7.

$$\sqrt{\frac{630+7^{2}}{5-1}}$$

Calcula 7 á potencia de 2 e obtén 49.

$$\sqrt{\frac{630+49}{5-1}}$$

Suma 630 e 49 para obter 679.

$$\sqrt{\frac{679}{5-1}}$$

Resta 1 de 5 para obter 4.

$$\sqrt{\frac{679}{4}}$$

Reescribe a raíz cadrada da división \sqrt{\frac{679}{4}} como a división de raíces cadradas \frac{\sqrt{679}}{\sqrt{4}}.

$$\frac{\sqrt{679}}{\sqrt{4}}$$

Calcular a raíz cadrada de 4 e obter 2.

$$\frac{\sqrt{679}}{2}$$