Resolver sqrt{(2.5*10^-4)^2+(0.1*10^-2)^2}

$$\sqrt { ( 2.5 \times 10 ^ { - 4 } ) ^ { 2 } + ( 0.1 \times 10 ^ { - 2 } ) ^ { 2 } }$$

Calcular

$$\frac{\sqrt{17}}{4000}\approx 0.001030776$$

Pasos da solución

Calcula 10 á potencia de -4 e obtén \frac{1}{10000}.

$$\sqrt{\left(2.5\times \frac{1}{10000}\right)^{2}+\left(0.1\times 10^{-2}\right)^{2}}$$

Multiplica 2.5 e \frac{1}{10000} para obter \frac{1}{4000}.

$$\sqrt{\left(\frac{1}{4000}\right)^{2}+\left(0.1\times 10^{-2}\right)^{2}}$$

Calcula \frac{1}{4000} á potencia de 2 e obtén \frac{1}{16000000}.

$$\sqrt{\frac{1}{16000000}+\left(0.1\times 10^{-2}\right)^{2}}$$

Calcula 10 á potencia de -2 e obtén \frac{1}{100}.

$$\sqrt{\frac{1}{16000000}+\left(0.1\times \frac{1}{100}\right)^{2}}$$

Multiplica 0.1 e \frac{1}{100} para obter \frac{1}{1000}.

$$\sqrt{\frac{1}{16000000}+\left(\frac{1}{1000}\right)^{2}}$$

Calcula \frac{1}{1000} á potencia de 2 e obtén \frac{1}{1000000}.

$$\sqrt{\frac{1}{16000000}+\frac{1}{1000000}}$$

Suma \frac{1}{16000000} e \frac{1}{1000000} para obter \frac{17}{16000000}.

$$\sqrt{\frac{17}{16000000}}$$

Reescribe a raíz cadrada da división \sqrt{\frac{17}{16000000}} como a división de raíces cadradas \frac{\sqrt{17}}{\sqrt{16000000}}.

$$\frac{\sqrt{17}}{\sqrt{16000000}}$$

Calcular a raíz cadrada de 16000000 e obter 4000.

$$\frac{\sqrt{17}}{4000}$$