Solve sqrt{(229*10^-4)^2+(905*10^-3)^2}

$$\sqrt { ( 229 \cdot 10 ^ { - 4 } ) ^ { 2 } + ( 905 \cdot 10 ^ { - 3 } ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{81954941}}{10000}\approx 0.905289683$$

Solution Steps

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

$$\sqrt{\left(229\times \frac{1}{10000}\right)^{2}+\left(905\times 10^{-3}\right)^{2}}$$

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

$$\sqrt{\left(\frac{229}{10000}\right)^{2}+\left(905\times 10^{-3}\right)^{2}}$$

Calculate \frac{229}{10000} to the power of 2 and get \frac{52441}{100000000}.

$$\sqrt{\frac{52441}{100000000}+\left(905\times 10^{-3}\right)^{2}}$$

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

$$\sqrt{\frac{52441}{100000000}+\left(905\times \frac{1}{1000}\right)^{2}}$$

Multiply 905 and \frac{1}{1000} to get \frac{181}{200}.

$$\sqrt{\frac{52441}{100000000}+\left(\frac{181}{200}\right)^{2}}$$

Calculate \frac{181}{200} to the power of 2 and get \frac{32761}{40000}.

$$\sqrt{\frac{52441}{100000000}+\frac{32761}{40000}}$$

Add \frac{52441}{100000000} and \frac{32761}{40000} to get \frac{81954941}{100000000}.

$$\sqrt{\frac{81954941}{100000000}}$$

Rewrite the square root of the division \sqrt{\frac{81954941}{100000000}} as the division of square roots \frac{\sqrt{81954941}}{\sqrt{100000000}}.

$$\frac{\sqrt{81954941}}{\sqrt{100000000}}$$

Calculate the square root of 100000000 and get 10000.

$$\frac{\sqrt{81954941}}{10000}$$