Solve sqrt{8/5+73div573910}

$$\sqrt { \frac { 8 } { 5 } + 73 \div 573910 }$$

Evaluate

$$\frac{\sqrt{527038196390}}{573910}\approx 1.264961342$$

Solution Steps

Least common multiple of 5 and 573910 is 573910. Convert \frac{8}{5} and \frac{73}{573910} to fractions with denominator 573910.

$$\sqrt{\frac{918256}{573910}+\frac{73}{573910}}$$

Since \frac{918256}{573910} and \frac{73}{573910} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{918256+73}{573910}}$$

Add 918256 and 73 to get 918329.

$$\sqrt{\frac{918329}{573910}}$$

Rewrite the square root of the division \sqrt{\frac{918329}{573910}} as the division of square roots \frac{\sqrt{918329}}{\sqrt{573910}}.

$$\frac{\sqrt{918329}}{\sqrt{573910}}$$

Rationalize the denominator of \frac{\sqrt{918329}}{\sqrt{573910}} by multiplying numerator and denominator by \sqrt{573910}.

$$\frac{\sqrt{918329}\sqrt{573910}}{\left(\sqrt{573910}\right)^{2}}$$

The square of \sqrt{573910} is 573910.

$$\frac{\sqrt{918329}\sqrt{573910}}{573910}$$

To multiply \sqrt{918329} and \sqrt{573910}, multiply the numbers under the square root.

$$\frac{\sqrt{527038196390}}{573910}$$