Solve frac{4sqrt{5}}{5000}*sqrt{510/293}

$$\frac { 4 \sqrt { 5 } } { 5000 } \times \sqrt { \frac { 510 } { 293 } }$$

Evaluate

$$\frac{\sqrt{29886}}{73250}\approx 0.002360078$$

Solution Steps

Divide 4\sqrt{5} by 5000 to get \frac{1}{1250}\sqrt{5}.

$$\frac{1}{1250}\sqrt{5}\sqrt{\frac{510}{293}}$$

Rewrite the square root of the division \sqrt{\frac{510}{293}} as the division of square roots \frac{\sqrt{510}}{\sqrt{293}}.

$$\frac{1}{1250}\sqrt{5}\times \frac{\sqrt{510}}{\sqrt{293}}$$

Rationalize the denominator of \frac{\sqrt{510}}{\sqrt{293}} by multiplying numerator and denominator by \sqrt{293}.

$$\frac{1}{1250}\sqrt{5}\times \frac{\sqrt{510}\sqrt{293}}{\left(\sqrt{293}\right)^{2}}$$

The square of \sqrt{293} is 293.

$$\frac{1}{1250}\sqrt{5}\times \frac{\sqrt{510}\sqrt{293}}{293}$$

To multiply \sqrt{510} and \sqrt{293}, multiply the numbers under the square root.

$$\frac{1}{1250}\sqrt{5}\times \frac{\sqrt{149430}}{293}$$

Multiply \frac{1}{1250} times \frac{\sqrt{149430}}{293} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{149430}}{1250\times 293}\sqrt{5}$$

Multiply 1250 and 293 to get 366250.

$$\frac{\sqrt{149430}}{366250}\sqrt{5}$$

Express \frac{\sqrt{149430}}{366250}\sqrt{5} as a single fraction.

$$\frac{\sqrt{149430}\sqrt{5}}{366250}$$

Factor 149430=5\times 29886. Rewrite the square root of the product \sqrt{5\times 29886} as the product of square roots \sqrt{5}\sqrt{29886}.

$$\frac{\sqrt{5}\sqrt{29886}\sqrt{5}}{366250}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{5\sqrt{29886}}{366250}$$

Divide 5\sqrt{29886} by 366250 to get \frac{1}{73250}\sqrt{29886}.

$$\frac{1}{73250}\sqrt{29886}$$