Solve sqrt{0.012/20}

$$\sqrt{ \frac{ 0.012 }{ 20 } }$$

Evaluate

$$\frac{\sqrt{6}}{100}\approx 0.024494897$$

Solution Steps

Expand \frac{0.012}{20} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{12}{20000}}$$

Reduce the fraction \frac{12}{20000} to lowest terms by extracting and canceling out 4.

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

Rewrite the square root of the division \sqrt{\frac{3}{5000}} as the division of square roots \frac{\sqrt{3}}{\sqrt{5000}}.

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

Factor 5000=50^{2}\times 2. Rewrite the square root of the product \sqrt{50^{2}\times 2} as the product of square roots \sqrt{50^{2}}\sqrt{2}. Take the square root of 50^{2}.

$$\frac{\sqrt{3}}{50\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{3}}{50\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{3}\sqrt{2}}{50\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{3}\sqrt{2}}{50\times 2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{50\times 2}$$

Multiply 50 and 2 to get 100.

$$\frac{\sqrt{6}}{100}$$