Solve sqrt{0.03/20}

$$\sqrt{ \frac{ 0.03 }{ 20 } }$$

Evaluate

$$\frac{\sqrt{15}}{100}\approx 0.038729833$$

Solution Steps

Expand \frac{0.03}{20} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{3}{2000}}$$

Rewrite the square root of the division \sqrt{\frac{3}{2000}} as the division of square roots \frac{\sqrt{3}}{\sqrt{2000}}.

$$\frac{\sqrt{3}}{\sqrt{2000}}$$

Factor 2000=20^{2}\times 5. Rewrite the square root of the product \sqrt{20^{2}\times 5} as the product of square roots \sqrt{20^{2}}\sqrt{5}. Take the square root of 20^{2}.

$$\frac{\sqrt{3}}{20\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{3}}{20\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{3}\sqrt{5}}{20\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{3}\sqrt{5}}{20\times 5}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{15}}{20\times 5}$$

Multiply 20 and 5 to get 100.

$$\frac{\sqrt{15}}{100}$$