Solve 5/6*4/sqrt{10}=

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

Evaluate

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

Solution Steps

Rationalize the denominator of \frac{4}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{5}{6}\times \frac{4\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

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

Divide 4\sqrt{10} by 10 to get \frac{2}{5}\sqrt{10}.

$$\frac{5}{6}\times \frac{2}{5}\sqrt{10}$$

Multiply \frac{5}{6} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 2}{6\times 5}\sqrt{10}$$

Cancel out 5 in both numerator and denominator.

$$\frac{2}{6}\sqrt{10}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}\sqrt{10}$$