Solve sqrt{300/373.475}=

$$\sqrt { \frac { 300 } { 373.475 } } =$$

Evaluate

$$\frac{20\sqrt{448170}}{14939}\approx 0.896251425$$

Solution Steps

Expand \frac{300}{373.475} by multiplying both numerator and the denominator by 1000.

$$\sqrt{\frac{300000}{373475}}$$

Reduce the fraction \frac{300000}{373475} to lowest terms by extracting and canceling out 25.

$$\sqrt{\frac{12000}{14939}}$$

Rewrite the square root of the division \sqrt{\frac{12000}{14939}} as the division of square roots \frac{\sqrt{12000}}{\sqrt{14939}}.

$$\frac{\sqrt{12000}}{\sqrt{14939}}$$

Factor 12000=20^{2}\times 30. Rewrite the square root of the product \sqrt{20^{2}\times 30} as the product of square roots \sqrt{20^{2}}\sqrt{30}. Take the square root of 20^{2}.

$$\frac{20\sqrt{30}}{\sqrt{14939}}$$

Rationalize the denominator of \frac{20\sqrt{30}}{\sqrt{14939}} by multiplying numerator and denominator by \sqrt{14939}.

$$\frac{20\sqrt{30}\sqrt{14939}}{\left(\sqrt{14939}\right)^{2}}$$

The square of \sqrt{14939} is 14939.

$$\frac{20\sqrt{30}\sqrt{14939}}{14939}$$

To multiply \sqrt{30} and \sqrt{14939}, multiply the numbers under the square root.

$$\frac{20\sqrt{448170}}{14939}$$