Resolver sqrt{0.1(-14*5%)^2+0.3(-2.5%)^2+0.4(2.5%)^2+0.2(5.5%)^2}

$$\sqrt { 0.1 ( - 14 \cdot 5 \% ) ^ { 2 } + 0.3 ( - 2.5 \% ) ^ { 2 } + 0.4 ( 2.5 \% ) ^ { 2 } + 0.2 ( 5.5 \% ) ^ { 2 } }$$

Calcular

$$\frac{\sqrt{200170}}{2000}\approx 0.22370181$$

Pasos da solución

Reduce a fracción \frac{5}{100} a termos máis baixos extraendo e cancelando 5.

$$\sqrt{0.1\left(-14\times \frac{1}{20}\right)^{2}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Multiplica -14 e \frac{1}{20} para obter -\frac{7}{10}.

$$\sqrt{0.1\left(-\frac{7}{10}\right)^{2}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Calcula -\frac{7}{10} á potencia de 2 e obtén \frac{49}{100}.

$$\sqrt{0.1\times \frac{49}{100}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Multiplica 0.1 e \frac{49}{100} para obter \frac{49}{1000}.

$$\sqrt{\frac{49}{1000}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

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

$$\sqrt{\frac{49}{1000}+0.3\left(-\frac{25}{1000}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

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

$$\sqrt{\frac{49}{1000}+0.3\left(-\frac{1}{40}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

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

$$\sqrt{\frac{49}{1000}+0.3\times \frac{1}{1600}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

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

$$\sqrt{\frac{49}{1000}+\frac{3}{16000}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Suma \frac{49}{1000} e \frac{3}{16000} para obter \frac{787}{16000}.

$$\sqrt{\frac{787}{16000}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

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

$$\sqrt{\frac{787}{16000}+0.4\times \left(\frac{25}{1000}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

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

$$\sqrt{\frac{787}{16000}+0.4\times \left(\frac{1}{40}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

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

$$\sqrt{\frac{787}{16000}+0.4\times \frac{1}{1600}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

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

$$\sqrt{\frac{787}{16000}+\frac{1}{4000}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

Suma \frac{787}{16000} e \frac{1}{4000} para obter \frac{791}{16000}.

$$\sqrt{\frac{791}{16000}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

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

$$\sqrt{\frac{791}{16000}+0.2\times \left(\frac{55}{1000}\right)^{2}}$$

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

$$\sqrt{\frac{791}{16000}+0.2\times \left(\frac{11}{200}\right)^{2}}$$

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

$$\sqrt{\frac{791}{16000}+0.2\times \frac{121}{40000}}$$

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

$$\sqrt{\frac{791}{16000}+\frac{121}{200000}}$$

Suma \frac{791}{16000} e \frac{121}{200000} para obter \frac{20017}{400000}.

$$\sqrt{\frac{20017}{400000}}$$

Reescribe a raíz cadrada da división \sqrt{\frac{20017}{400000}} como a división de raíces cadradas \frac{\sqrt{20017}}{\sqrt{400000}}.

$$\frac{\sqrt{20017}}{\sqrt{400000}}$$

Factoriza 400000=200^{2}\times 10. Reescribe a raíz cadrada do produto \sqrt{200^{2}\times 10} como o produto de raíces cadradas \sqrt{200^{2}}\sqrt{10}. Obtén a raíz cadrada de 200^{2}.

$$\frac{\sqrt{20017}}{200\sqrt{10}}$$

Racionaliza o denominador de \frac{\sqrt{20017}}{200\sqrt{10}} mediante a multiplicación do numerador e o denominador por \sqrt{10}.

$$\frac{\sqrt{20017}\sqrt{10}}{200\left(\sqrt{10}\right)^{2}}$$

O cadrado de \sqrt{10} é 10.

$$\frac{\sqrt{20017}\sqrt{10}}{200\times 10}$$

Para multiplicar \sqrt{20017} e \sqrt{10}, multiplica os números baixo a raíz cadrada.

$$\frac{\sqrt{200170}}{200\times 10}$$

Multiplica 200 e 10 para obter 2000.

$$\frac{\sqrt{200170}}{2000}$$