Resolver sqrt{0.1(-14.5%)^2+0.3(-2.5%)^2+0.4(2.5%)^2+0.2(5.5%)^2}

$$\sqrt { 0.1 ( - 14.5 \% ) ^ { 2 } + 0.3 ( - 2.5 \% ) ^ { 2 } + 0.4 ( 2.5 \% ) ^ { 2 } + 0.2 ( 5.5 \% ) ^ { 2 } }$$

Calcular

$$\frac{\sqrt{3145}}{1000}\approx 0.0560803$$

Pasos da solución

Expande \frac{14.5}{100} multiplicando o numerador e o denominador por 10.

$$\sqrt{0.1\left(-\frac{145}{1000}\right)^{2}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Reduce a fracción \frac{145}{1000} a termos máis baixos extraendo e cancelando 5.

$$\sqrt{0.1\left(-\frac{29}{200}\right)^{2}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Calcula -\frac{29}{200} á potencia de 2 e obtén \frac{841}{40000}.

$$\sqrt{0.1\times \frac{841}{40000}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Multiplica 0.1 e \frac{841}{40000} para obter \frac{841}{400000}.

$$\sqrt{\frac{841}{400000}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Expande \frac{2.5}{100} multiplicando o numerador e o denominador por 10.

$$\sqrt{\frac{841}{400000}+0.3\left(-\frac{25}{1000}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Reduce a fracción \frac{25}{1000} a termos máis baixos extraendo e cancelando 25.

$$\sqrt{\frac{841}{400000}+0.3\left(-\frac{1}{40}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Calcula -\frac{1}{40} á potencia de 2 e obtén \frac{1}{1600}.

$$\sqrt{\frac{841}{400000}+0.3\times \frac{1}{1600}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Multiplica 0.3 e \frac{1}{1600} para obter \frac{3}{16000}.

$$\sqrt{\frac{841}{400000}+\frac{3}{16000}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Suma \frac{841}{400000} e \frac{3}{16000} para obter \frac{229}{100000}.

$$\sqrt{\frac{229}{100000}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Expande \frac{2.5}{100} multiplicando o numerador e o denominador por 10.

$$\sqrt{\frac{229}{100000}+0.4\times \left(\frac{25}{1000}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Reduce a fracción \frac{25}{1000} a termos máis baixos extraendo e cancelando 25.

$$\sqrt{\frac{229}{100000}+0.4\times \left(\frac{1}{40}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Calcula \frac{1}{40} á potencia de 2 e obtén \frac{1}{1600}.

$$\sqrt{\frac{229}{100000}+0.4\times \frac{1}{1600}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Multiplica 0.4 e \frac{1}{1600} para obter \frac{1}{4000}.

$$\sqrt{\frac{229}{100000}+\frac{1}{4000}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Suma \frac{229}{100000} e \frac{1}{4000} para obter \frac{127}{50000}.

$$\sqrt{\frac{127}{50000}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Expande \frac{5.5}{100} multiplicando o numerador e o denominador por 10.

$$\sqrt{\frac{127}{50000}+0.2\times \left(\frac{55}{1000}\right)^{2}}$$

Reduce a fracción \frac{55}{1000} a termos máis baixos extraendo e cancelando 5.

$$\sqrt{\frac{127}{50000}+0.2\times \left(\frac{11}{200}\right)^{2}}$$

Calcula \frac{11}{200} á potencia de 2 e obtén \frac{121}{40000}.

$$\sqrt{\frac{127}{50000}+0.2\times \frac{121}{40000}}$$

Multiplica 0.2 e \frac{121}{40000} para obter \frac{121}{200000}.

$$\sqrt{\frac{127}{50000}+\frac{121}{200000}}$$

Suma \frac{127}{50000} e \frac{121}{200000} para obter \frac{629}{200000}.

$$\sqrt{\frac{629}{200000}}$$

Reescribe a raíz cadrada da división \sqrt{\frac{629}{200000}} como a división de raíces cadradas \frac{\sqrt{629}}{\sqrt{200000}}.

$$\frac{\sqrt{629}}{\sqrt{200000}}$$

Factoriza 200000=200^{2}\times 5. Reescribe a raíz cadrada do produto \sqrt{200^{2}\times 5} como o produto de raíces cadradas \sqrt{200^{2}}\sqrt{5}. Obtén a raíz cadrada de 200^{2}.

$$\frac{\sqrt{629}}{200\sqrt{5}}$$

Racionaliza o denominador de \frac{\sqrt{629}}{200\sqrt{5}} mediante a multiplicación do numerador e o denominador por \sqrt{5}.

$$\frac{\sqrt{629}\sqrt{5}}{200\left(\sqrt{5}\right)^{2}}$$

O cadrado de \sqrt{5} é 5.

$$\frac{\sqrt{629}\sqrt{5}}{200\times 5}$$

Para multiplicar \sqrt{629} e \sqrt{5}, multiplica os números baixo a raíz cadrada.

$$\frac{\sqrt{3145}}{200\times 5}$$

Multiplica 200 e 5 para obter 1000.

$$\frac{\sqrt{3145}}{1000}$$