Solve sqrt{1.8*10^-6}

$$\sqrt { 1.8 \times 10 ^ { - 6 } }$$

Evaluate

$$\frac{3\sqrt{5}}{5000}\approx 0.001341641$$

Solution Steps

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

$$\sqrt{1.8\times \frac{1}{1000000}}$$

Multiply 1.8 and \frac{1}{1000000} to get \frac{9}{5000000}.

$$\sqrt{\frac{9}{5000000}}$$

Rewrite the square root of the division \sqrt{\frac{9}{5000000}} as the division of square roots \frac{\sqrt{9}}{\sqrt{5000000}}.

$$\frac{\sqrt{9}}{\sqrt{5000000}}$$

Calculate the square root of 9 and get 3.

$$\frac{3}{\sqrt{5000000}}$$

Factor 5000000=1000^{2}\times 5. Rewrite the square root of the product \sqrt{1000^{2}\times 5} as the product of square roots \sqrt{1000^{2}}\sqrt{5}. Take the square root of 1000^{2}.

$$\frac{3}{1000\sqrt{5}}$$

Rationalize the denominator of \frac{3}{1000\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{3\sqrt{5}}{1000\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{3\sqrt{5}}{1000\times 5}$$

Multiply 1000 and 5 to get 5000.

$$\frac{3\sqrt{5}}{5000}$$