Solve 5/10sqrt{13/6}

$$\frac { 5 } { 10 } \sqrt { \frac { 13 } { 6 } }$$

Evaluate

$$\frac{\sqrt{78}}{12}\approx 0.735980072$$

Solution Steps

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}\sqrt{\frac{13}{6}}$$

Rewrite the square root of the division \sqrt{\frac{13}{6}} as the division of square roots \frac{\sqrt{13}}{\sqrt{6}}.

$$\frac{1}{2}\times \frac{\sqrt{13}}{\sqrt{6}}$$

Rationalize the denominator of \frac{\sqrt{13}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{1}{2}\times \frac{\sqrt{13}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{1}{2}\times \frac{\sqrt{13}\sqrt{6}}{6}$$

To multiply \sqrt{13} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{1}{2}\times \frac{\sqrt{78}}{6}$$

Multiply \frac{1}{2} times \frac{\sqrt{78}}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{78}}{2\times 6}$$

Multiply 2 and 6 to get 12.

$$\frac{\sqrt{78}}{12}$$