Solve sqrt{(2.29*10^-4)^2+(9.05*10^-3)^2}

$$\sqrt { ( 2.29 \cdot 10 ^ { - 4 } ) ^ { 2 } + ( 9.05 \cdot 10 ^ { - 3 } ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{81954941}}{1000000}\approx 0.009052897$$

Solution Steps

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

$$\sqrt{\left(2.29\times \frac{1}{10000}\right)^{2}+\left(9.05\times 10^{-3}\right)^{2}}$$

Multiply 2.29 and \frac{1}{10000} to get \frac{229}{1000000}.

$$\sqrt{\left(\frac{229}{1000000}\right)^{2}+\left(9.05\times 10^{-3}\right)^{2}}$$

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

$$\sqrt{\frac{52441}{1000000000000}+\left(9.05\times 10^{-3}\right)^{2}}$$

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

$$\sqrt{\frac{52441}{1000000000000}+\left(9.05\times \frac{1}{1000}\right)^{2}}$$

Multiply 9.05 and \frac{1}{1000} to get \frac{181}{20000}.

$$\sqrt{\frac{52441}{1000000000000}+\left(\frac{181}{20000}\right)^{2}}$$

Calculate \frac{181}{20000} to the power of 2 and get \frac{32761}{400000000}.

$$\sqrt{\frac{52441}{1000000000000}+\frac{32761}{400000000}}$$

Add \frac{52441}{1000000000000} and \frac{32761}{400000000} to get \frac{81954941}{1000000000000}.

$$\sqrt{\frac{81954941}{1000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{81954941}{1000000000000}} as the division of square roots \frac{\sqrt{81954941}}{\sqrt{1000000000000}}.

$$\frac{\sqrt{81954941}}{\sqrt{1000000000000}}$$

Calculate the square root of 1000000000000 and get 1000000.

$$\frac{\sqrt{81954941}}{1000000}$$