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

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

Evaluate

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

Solution Steps

Calculate 10 to the power of -4 and get \frac{1}{10000}.

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

Multiply 2.5 and \frac{1}{10000} to get \frac{1}{4000}.

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

Calculate \frac{1}{4000} to the power of 2 and get \frac{1}{16000000}.

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

Calculate 10 to the power of -2 and get \frac{1}{100}.

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

Multiply 0.1 and \frac{1}{100} to get \frac{1}{1000}.

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

Calculate \frac{1}{1000} to the power of 2 and get \frac{1}{1000000}.

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

Add \frac{1}{16000000} and \frac{1}{1000000} to get \frac{17}{16000000}.

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

Rewrite the square root of the division \sqrt{\frac{17}{16000000}} as the division of square roots \frac{\sqrt{17}}{\sqrt{16000000}}.

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

Calculate the square root of 16000000 and get 4000.

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