Solve sqrt{(0.5*10^-2)^2+(0.5sqrt{3}*10^-2)^2}

$$\sqrt { ( 0.5 \times 10 ^ { - 2 } ) ^ { 2 } + ( 0.5 \sqrt { 3 } \times 10 ^ { - 2 } ) ^ { 2 } }$$

Evaluate

$$0.01$$

Solution Steps

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

$$\sqrt{\left(0.5\times \frac{1}{100}\right)^{2}+\left(0.5\sqrt{3}\times 10^{-2}\right)^{2}}$$

Multiply 0.5 and \frac{1}{100} to get \frac{1}{200}.

$$\sqrt{\left(\frac{1}{200}\right)^{2}+\left(0.5\sqrt{3}\times 10^{-2}\right)^{2}}$$

Calculate \frac{1}{200} to the power of 2 and get \frac{1}{40000}.

$$\sqrt{\frac{1}{40000}+\left(0.5\sqrt{3}\times 10^{-2}\right)^{2}}$$

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

$$\sqrt{\frac{1}{40000}+\left(0.5\sqrt{3}\times \frac{1}{100}\right)^{2}}$$

Multiply 0.5 and \frac{1}{100} to get \frac{1}{200}.

$$\sqrt{\frac{1}{40000}+\left(\frac{1}{200}\sqrt{3}\right)^{2}}$$

Expand \left(\frac{1}{200}\sqrt{3}\right)^{2}.

$$\sqrt{\frac{1}{40000}+\left(\frac{1}{200}\right)^{2}\left(\sqrt{3}\right)^{2}}$$

Calculate \frac{1}{200} to the power of 2 and get \frac{1}{40000}.

$$\sqrt{\frac{1}{40000}+\frac{1}{40000}\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{\frac{1}{40000}+\frac{1}{40000}\times 3}$$

Multiply \frac{1}{40000} and 3 to get \frac{3}{40000}.

$$\sqrt{\frac{1}{40000}+\frac{3}{40000}}$$

Add \frac{1}{40000} and \frac{3}{40000} to get \frac{1}{10000}.

$$\sqrt{\frac{1}{10000}}$$

Rewrite the square root of the division \frac{1}{10000} as the division of square roots \frac{\sqrt{1}}{\sqrt{10000}}. Take the square root of both numerator and denominator.

$$\frac{1}{100}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 5 ^ {2}} = 0.01$$