Solve sqrt{0.001^2*6/5}

$$\sqrt{ \frac{ { 0.001 }^{ 2 } \times 6 }{ 5 } }$$

Evaluate

$$\frac{\sqrt{30}}{5000}\approx 0.001095445$$

Solution Steps

Calculate 0.001 to the power of 2 and get 0.000001.

$$\sqrt{\frac{0.000001\times 6}{5}}$$

Multiply 0.000001 and 6 to get 0.000006.

$$\sqrt{\frac{0.000006}{5}}$$

Expand \frac{0.000006}{5} by multiplying both numerator and the denominator by 1000000.

$$\sqrt{\frac{6}{5000000}}$$

Reduce the fraction \frac{6}{5000000} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{3}{2500000}}$$

Rewrite the square root of the division \sqrt{\frac{3}{2500000}} as the division of square roots \frac{\sqrt{3}}{\sqrt{2500000}}.

$$\frac{\sqrt{3}}{\sqrt{2500000}}$$

Factor 2500000=500^{2}\times 10. Rewrite the square root of the product \sqrt{500^{2}\times 10} as the product of square roots \sqrt{500^{2}}\sqrt{10}. Take the square root of 500^{2}.

$$\frac{\sqrt{3}}{500\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{3}}{500\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{3}\sqrt{10}}{500\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{3}\sqrt{10}}{500\times 10}$$

To multiply \sqrt{3} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{30}}{500\times 10}$$

Multiply 500 and 10 to get 5000.

$$\frac{\sqrt{30}}{5000}$$