Solve sqrt{300/373475}=

$$\sqrt { \frac { 300 } { 373475 } } =$$

Evaluate

$$\frac{2\sqrt{44817}}{14939}\approx 0.028341959$$

Solution Steps

Reduce the fraction \frac{300}{373475} to lowest terms by extracting and canceling out 25.

$$\sqrt{\frac{12}{14939}}$$

Rewrite the square root of the division \sqrt{\frac{12}{14939}} as the division of square roots \frac{\sqrt{12}}{\sqrt{14939}}.

$$\frac{\sqrt{12}}{\sqrt{14939}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{2\sqrt{3}}{\sqrt{14939}}$$

Rationalize the denominator of \frac{2\sqrt{3}}{\sqrt{14939}} by multiplying numerator and denominator by \sqrt{14939}.

$$\frac{2\sqrt{3}\sqrt{14939}}{\left(\sqrt{14939}\right)^{2}}$$

The square of \sqrt{14939} is 14939.

$$\frac{2\sqrt{3}\sqrt{14939}}{14939}$$

To multiply \sqrt{3} and \sqrt{14939}, multiply the numbers under the square root.

$$\frac{2\sqrt{44817}}{14939}$$