Solve sqrt{left(8.5*10^-4right)^2+left(8.5*10^-4right)^2}

$$\sqrt{ { \left(8.5 \times { 10 }^{ -4 } \right) }^{ 2 } + { \left(8.5 \times { 10 }^{ -4 } \right) }^{ 2 } }$$

Evaluate

$$\frac{17\sqrt{2}}{20000}\approx 0.001202082$$

Solution Steps

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

$$\sqrt{\left(8.5\times \frac{1}{10000}\right)^{2}+\left(8.5\times 10^{-4}\right)^{2}}$$

Multiply 8.5 and \frac{1}{10000} to get \frac{17}{20000}.

$$\sqrt{\left(\frac{17}{20000}\right)^{2}+\left(8.5\times 10^{-4}\right)^{2}}$$

Calculate \frac{17}{20000} to the power of 2 and get \frac{289}{400000000}.

$$\sqrt{\frac{289}{400000000}+\left(8.5\times 10^{-4}\right)^{2}}$$

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

$$\sqrt{\frac{289}{400000000}+\left(8.5\times \frac{1}{10000}\right)^{2}}$$

Multiply 8.5 and \frac{1}{10000} to get \frac{17}{20000}.

$$\sqrt{\frac{289}{400000000}+\left(\frac{17}{20000}\right)^{2}}$$

Calculate \frac{17}{20000} to the power of 2 and get \frac{289}{400000000}.

$$\sqrt{\frac{289}{400000000}+\frac{289}{400000000}}$$

Add \frac{289}{400000000} and \frac{289}{400000000} to get \frac{289}{200000000}.

$$\sqrt{\frac{289}{200000000}}$$

Rewrite the square root of the division \sqrt{\frac{289}{200000000}} as the division of square roots \frac{\sqrt{289}}{\sqrt{200000000}}.

$$\frac{\sqrt{289}}{\sqrt{200000000}}$$

Calculate the square root of 289 and get 17.

$$\frac{17}{\sqrt{200000000}}$$

Factor 200000000=10000^{2}\times 2. Rewrite the square root of the product \sqrt{10000^{2}\times 2} as the product of square roots \sqrt{10000^{2}}\sqrt{2}. Take the square root of 10000^{2}.

$$\frac{17}{10000\sqrt{2}}$$

Rationalize the denominator of \frac{17}{10000\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{17\sqrt{2}}{10000\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{17\sqrt{2}}{10000\times 2}$$

Multiply 10000 and 2 to get 20000.

$$\frac{17\sqrt{2}}{20000}$$