Solve sqrt{0.05872%}

$$\sqrt{ 0.05872 \% }$$

Evaluate

$$\frac{\sqrt{3670}}{2500}\approx 0.02423221$$

Solution Steps

Expand \frac{0.05872}{100} by multiplying both numerator and the denominator by 100000.

$$\sqrt{\frac{5872}{10000000}}$$

Reduce the fraction \frac{5872}{10000000} to lowest terms by extracting and canceling out 16.

$$\sqrt{\frac{367}{625000}}$$

Rewrite the square root of the division \sqrt{\frac{367}{625000}} as the division of square roots \frac{\sqrt{367}}{\sqrt{625000}}.

$$\frac{\sqrt{367}}{\sqrt{625000}}$$

Factor 625000=250^{2}\times 10. Rewrite the square root of the product \sqrt{250^{2}\times 10} as the product of square roots \sqrt{250^{2}}\sqrt{10}. Take the square root of 250^{2}.

$$\frac{\sqrt{367}}{250\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{367}}{250\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{367}\sqrt{10}}{250\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{367}\sqrt{10}}{250\times 10}$$

To multiply \sqrt{367} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{3670}}{250\times 10}$$

Multiply 250 and 10 to get 2500.

$$\frac{\sqrt{3670}}{2500}$$