Solve 5/6:frac{sqrt{10}}{4}=

$$\frac { 5 } { 6 } : \frac { \sqrt { 10 } } { 4 } =$$

Evaluate

$$\frac{\sqrt{10}}{3}\approx 1.054092553$$

Solution Steps

Divide \frac{5}{6} by \frac{\sqrt{10}}{4} by multiplying \frac{5}{6} by the reciprocal of \frac{\sqrt{10}}{4}.

$$\frac{5\times 4}{6\sqrt{10}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{2\times 5}{3\sqrt{10}}$$

Multiply 2 and 5 to get 10.

$$\frac{10}{3\sqrt{10}}$$

Rationalize the denominator of \frac{10}{3\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{10\sqrt{10}}{3\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{10\sqrt{10}}{3\times 10}$$

Cancel out 10 in both numerator and denominator.

$$\frac{\sqrt{10}}{3}$$