Solve sqrt{1.8*10^-5*0.2}

$$\sqrt { 1.8 \times 10 ^ { - 5 } \times 0.2 }$$

Evaluate

$$\frac{3\sqrt{10}}{5000}\approx 0.001897367$$

Solution Steps

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$\sqrt{1.8\times \frac{1}{100000}\times 0.2}$$

Multiply 1.8 and \frac{1}{100000} to get \frac{9}{500000}.

$$\sqrt{\frac{9}{500000}\times 0.2}$$

Multiply \frac{9}{500000} and 0.2 to get \frac{9}{2500000}.

$$\sqrt{\frac{9}{2500000}}$$

Rewrite the square root of the division \sqrt{\frac{9}{2500000}} as the division of square roots \frac{\sqrt{9}}{\sqrt{2500000}}.

$$\frac{\sqrt{9}}{\sqrt{2500000}}$$

Calculate the square root of 9 and get 3.

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

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}.

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

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

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

The square of \sqrt{10} is 10.

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

Multiply 500 and 10 to get 5000.

$$\frac{3\sqrt{10}}{5000}$$