Solve sqrt{80*10^-6}-sqrt{20*10^-6}

$$\sqrt { 80 \times 10 ^ { - 6 } } - \sqrt { 20 \times 10 ^ { - 6 } }$$

Evaluate

$$\frac{\sqrt{5}}{500}\approx 0.004472136$$

Short Solution Steps

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$\sqrt{80\times \frac{1}{1000000}}-\sqrt{20\times 10^{-6}}$$

Multiply 80 and \frac{1}{1000000} to get \frac{1}{12500}.

$$\sqrt{\frac{1}{12500}}-\sqrt{20\times 10^{-6}}$$

Rewrite the square root of the division \sqrt{\frac{1}{12500}} as the division of square roots \frac{\sqrt{1}}{\sqrt{12500}}.

$$\frac{\sqrt{1}}{\sqrt{12500}}-\sqrt{20\times 10^{-6}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{12500}}-\sqrt{20\times 10^{-6}}$$

Factor 12500=50^{2}\times 5. Rewrite the square root of the product \sqrt{50^{2}\times 5} as the product of square roots \sqrt{50^{2}}\sqrt{5}. Take the square root of 50^{2}.

$$\frac{1}{50\sqrt{5}}-\sqrt{20\times 10^{-6}}$$

Rationalize the denominator of \frac{1}{50\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{5}}{50\left(\sqrt{5}\right)^{2}}-\sqrt{20\times 10^{-6}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{5}}{50\times 5}-\sqrt{20\times 10^{-6}}$$

Multiply 50 and 5 to get 250.

$$\frac{\sqrt{5}}{250}-\sqrt{20\times 10^{-6}}$$

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$\frac{\sqrt{5}}{250}-\sqrt{20\times \frac{1}{1000000}}$$

Multiply 20 and \frac{1}{1000000} to get \frac{1}{50000}.

$$\frac{\sqrt{5}}{250}-\sqrt{\frac{1}{50000}}$$

Rewrite the square root of the division \sqrt{\frac{1}{50000}} as the division of square roots \frac{\sqrt{1}}{\sqrt{50000}}.

$$\frac{\sqrt{5}}{250}-\frac{\sqrt{1}}{\sqrt{50000}}$$

Calculate the square root of 1 and get 1.

$$\frac{\sqrt{5}}{250}-\frac{1}{\sqrt{50000}}$$

Factor 50000=100^{2}\times 5. Rewrite the square root of the product \sqrt{100^{2}\times 5} as the product of square roots \sqrt{100^{2}}\sqrt{5}. Take the square root of 100^{2}.

$$\frac{\sqrt{5}}{250}-\frac{1}{100\sqrt{5}}$$

Rationalize the denominator of \frac{1}{100\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{5}}{250}-\frac{\sqrt{5}}{100\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{5}}{250}-\frac{\sqrt{5}}{100\times 5}$$

Multiply 100 and 5 to get 500.

$$\frac{\sqrt{5}}{250}-\frac{\sqrt{5}}{500}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 250 and 500 is 500. Multiply \frac{\sqrt{5}}{250} times \frac{2}{2}.

$$\frac{2\sqrt{5}}{500}-\frac{\sqrt{5}}{500}$$

Since \frac{2\sqrt{5}}{500} and \frac{\sqrt{5}}{500} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\sqrt{5}-\sqrt{5}}{500}$$

Do the calculations in 2\sqrt{5}-\sqrt{5}.

$$\frac{\sqrt{5}}{500}$$