Resolver sqrt{frac{left(3.96-3.998right)^2+left(3.98-3.998right)^2+left(3.95-3.998right)^2+left(4.03-3.998right)^2+{left(3.99-3.998right)}^{2}+{left(4.03-3.998right)}^{2}+{left(4.02-3.998right)}^2+{left(3.99-3.998right)}^2+{left(4.04-3.998right)}^2+{left(3.99+3.998right)}^2}{90}}

$$\sqrt{ \frac{ { \left(3.96-3.998 \right) }^{ 2 } + { \left(3.98-3.998 \right) }^{ 2 } + { \left(3.95-3.998 \right) }^{ 2 } + { \left(4.03-3.998 \right) }^{ 2 } + { \left(3.99-3.998 \right) }^{ 2 } + { \left(4.03-3.998 \right) }^{ 2 } + { \left(4.02-3.998 \right) }^{ 2 } + { \left(3.99-3.998 \right) }^{ 2 } + { \left(4.04-3.998 \right) }^{ 2 } + { \left(3.99+3.998 \right) }^{ 2 } }{ 90 } }$$

Calcular

$$\frac{\sqrt{398854}}{750}\approx 0.842065186$$

Pasos da solución

Resta 3.998 de 3.96 para obter -0.038.

$$\sqrt{\frac{\left(-0.038\right)^{2}+\left(3.98-3.998\right)^{2}+\left(3.95-3.998\right)^{2}+\left(4.03-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.03-3.998\right)^{2}+\left(4.02-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Calcula -0.038 á potencia de 2 e obtén 0.001444.

$$\sqrt{\frac{0.001444+\left(3.98-3.998\right)^{2}+\left(3.95-3.998\right)^{2}+\left(4.03-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.03-3.998\right)^{2}+\left(4.02-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Resta 3.998 de 3.98 para obter -0.018.

$$\sqrt{\frac{0.001444+\left(-0.018\right)^{2}+\left(3.95-3.998\right)^{2}+\left(4.03-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.03-3.998\right)^{2}+\left(4.02-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Calcula -0.018 á potencia de 2 e obtén 0.000324.

$$\sqrt{\frac{0.001444+0.000324+\left(3.95-3.998\right)^{2}+\left(4.03-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.03-3.998\right)^{2}+\left(4.02-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Suma 0.001444 e 0.000324 para obter 0.001768.

$$\sqrt{\frac{0.001768+\left(3.95-3.998\right)^{2}+\left(4.03-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.03-3.998\right)^{2}+\left(4.02-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Resta 3.998 de 3.95 para obter -0.048.

$$\sqrt{\frac{0.001768+\left(-0.048\right)^{2}+\left(4.03-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.03-3.998\right)^{2}+\left(4.02-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Calcula -0.048 á potencia de 2 e obtén 0.002304.

$$\sqrt{\frac{0.001768+0.002304+\left(4.03-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.03-3.998\right)^{2}+\left(4.02-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Suma 0.001768 e 0.002304 para obter 0.004072.

$$\sqrt{\frac{0.004072+\left(4.03-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.03-3.998\right)^{2}+\left(4.02-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Resta 3.998 de 4.03 para obter 0.032.

$$\sqrt{\frac{0.004072+0.032^{2}+\left(3.99-3.998\right)^{2}+\left(4.03-3.998\right)^{2}+\left(4.02-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Calcula 0.032 á potencia de 2 e obtén 0.001024.

$$\sqrt{\frac{0.004072+0.001024+\left(3.99-3.998\right)^{2}+\left(4.03-3.998\right)^{2}+\left(4.02-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Suma 0.004072 e 0.001024 para obter 0.005096.

$$\sqrt{\frac{0.005096+\left(3.99-3.998\right)^{2}+\left(4.03-3.998\right)^{2}+\left(4.02-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Resta 3.998 de 3.99 para obter -0.008.

$$\sqrt{\frac{0.005096+\left(-0.008\right)^{2}+\left(4.03-3.998\right)^{2}+\left(4.02-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Calcula -0.008 á potencia de 2 e obtén 0.000064.

$$\sqrt{\frac{0.005096+0.000064+\left(4.03-3.998\right)^{2}+\left(4.02-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Suma 0.005096 e 0.000064 para obter 0.00516.

$$\sqrt{\frac{0.00516+\left(4.03-3.998\right)^{2}+\left(4.02-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Resta 3.998 de 4.03 para obter 0.032.

$$\sqrt{\frac{0.00516+0.032^{2}+\left(4.02-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Calcula 0.032 á potencia de 2 e obtén 0.001024.

$$\sqrt{\frac{0.00516+0.001024+\left(4.02-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Suma 0.00516 e 0.001024 para obter 0.006184.

$$\sqrt{\frac{0.006184+\left(4.02-3.998\right)^{2}+\left(3.99-3.998\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Resta 3.998 de 4.02 para obter 0.022.

$$\sqrt{\frac{0.006184+0.022^{2}+\left(3.99-3.998\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Calcula 0.022 á potencia de 2 e obtén 0.000484.

$$\sqrt{\frac{0.006184+0.000484+\left(3.99-3.998\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Suma 0.006184 e 0.000484 para obter 0.006668.

$$\sqrt{\frac{0.006668+\left(3.99-3.998\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Resta 3.998 de 3.99 para obter -0.008.

$$\sqrt{\frac{0.006668+\left(-0.008\right)^{2}+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Calcula -0.008 á potencia de 2 e obtén 0.000064.

$$\sqrt{\frac{0.006668+0.000064+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Suma 0.006668 e 0.000064 para obter 0.006732.

$$\sqrt{\frac{0.006732+\left(4.04-3.998\right)^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Resta 3.998 de 4.04 para obter 0.042.

$$\sqrt{\frac{0.006732+0.042^{2}+\left(3.99+3.998\right)^{2}}{90}}$$

Calcula 0.042 á potencia de 2 e obtén 0.001764.

$$\sqrt{\frac{0.006732+0.001764+\left(3.99+3.998\right)^{2}}{90}}$$

Suma 0.006732 e 0.001764 para obter 0.008496.

$$\sqrt{\frac{0.008496+\left(3.99+3.998\right)^{2}}{90}}$$

Suma 3.99 e 3.998 para obter 7.988.

$$\sqrt{\frac{0.008496+7.988^{2}}{90}}$$

Calcula 7.988 á potencia de 2 e obtén 63.808144.

$$\sqrt{\frac{0.008496+63.808144}{90}}$$

Suma 0.008496 e 63.808144 para obter 63.81664.

$$\sqrt{\frac{63.81664}{90}}$$

Expande \frac{63.81664}{90} multiplicando o numerador e o denominador por 100000.

$$\sqrt{\frac{6381664}{9000000}}$$

Reduce a fracción \frac{6381664}{9000000} a termos máis baixos extraendo e cancelando 32.

$$\sqrt{\frac{199427}{281250}}$$

Reescribe a raíz cadrada da división \sqrt{\frac{199427}{281250}} como a división de raíces cadradas \frac{\sqrt{199427}}{\sqrt{281250}}.

$$\frac{\sqrt{199427}}{\sqrt{281250}}$$

Factoriza 281250=375^{2}\times 2. Reescribe a raíz cadrada do produto \sqrt{375^{2}\times 2} como o produto de raíces cadradas \sqrt{375^{2}}\sqrt{2}. Obtén a raíz cadrada de 375^{2}.

$$\frac{\sqrt{199427}}{375\sqrt{2}}$$

Racionaliza o denominador de \frac{\sqrt{199427}}{375\sqrt{2}} mediante a multiplicación do numerador e o denominador por \sqrt{2}.

$$\frac{\sqrt{199427}\sqrt{2}}{375\left(\sqrt{2}\right)^{2}}$$

O cadrado de \sqrt{2} é 2.

$$\frac{\sqrt{199427}\sqrt{2}}{375\times 2}$$

Para multiplicar \sqrt{199427} e \sqrt{2}, multiplica os números baixo a raíz cadrada.

$$\frac{\sqrt{398854}}{375\times 2}$$

Multiplica 375 e 2 para obter 750.

$$\frac{\sqrt{398854}}{750}$$