Solve sqrt{0.212%}

$$\sqrt { 0.212 \% }$$

Evaluate

$$\frac{\sqrt{530}}{500}\approx 0.046043458$$

Solution Steps

Expand \frac{0.212}{100} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{212}{100000}}$$

Reduce the fraction \frac{212}{100000} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{53}{25000}}$$

Rewrite the square root of the division \sqrt{\frac{53}{25000}} as the division of square roots \frac{\sqrt{53}}{\sqrt{25000}}.

$$\frac{\sqrt{53}}{\sqrt{25000}}$$

Factor 25000=50^{2}\times 10. Rewrite the square root of the product \sqrt{50^{2}\times 10} as the product of square roots \sqrt{50^{2}}\sqrt{10}. Take the square root of 50^{2}.

$$\frac{\sqrt{53}}{50\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{53}}{50\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{53}\sqrt{10}}{50\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{53}\sqrt{10}}{50\times 10}$$

To multiply \sqrt{53} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{530}}{50\times 10}$$

Multiply 50 and 10 to get 500.

$$\frac{\sqrt{530}}{500}$$