Solve sqrt{(2,29*10^-4)^2+(1,05*10^-3)^2}

$$\sqrt { ( 2,29 \cdot 10 ^ { - 4 } ) ^ { 2 } + ( 1,05 \cdot 10 ^ { - 3 } ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{1154941}}{1000000}\approx 0.001074682$$

Solution Steps

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

$$\sqrt{\left(2,29\times \frac{1}{10000}\right)^{2}+\left(1,05\times 10^{-3}\right)^{2}}$$

Multiply 2,29 and \frac{1}{10000} to get \frac{229}{1000000}.

$$\sqrt{\left(\frac{229}{1000000}\right)^{2}+\left(1,05\times 10^{-3}\right)^{2}}$$

Calculate \frac{229}{1000000} to the power of 2 and get \frac{52441}{1000000000000}.

$$\sqrt{\frac{52441}{1000000000000}+\left(1,05\times 10^{-3}\right)^{2}}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\sqrt{\frac{52441}{1000000000000}+\left(1,05\times \frac{1}{1000}\right)^{2}}$$

Multiply 1,05 and \frac{1}{1000} to get \frac{21}{20000}.

$$\sqrt{\frac{52441}{1000000000000}+\left(\frac{21}{20000}\right)^{2}}$$

Calculate \frac{21}{20000} to the power of 2 and get \frac{441}{400000000}.

$$\sqrt{\frac{52441}{1000000000000}+\frac{441}{400000000}}$$

Add \frac{52441}{1000000000000} and \frac{441}{400000000} to get \frac{1154941}{1000000000000}.

$$\sqrt{\frac{1154941}{1000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{1154941}{1000000000000}} as the division of square roots \frac{\sqrt{1154941}}{\sqrt{1000000000000}}.

$$\frac{\sqrt{1154941}}{\sqrt{1000000000000}}$$

Calculate the square root of 1000000000000 and get 1000000.

$$\frac{\sqrt{1154941}}{1000000}$$