Solve sqrt{10/3}:sqrt{5/6}

$$\sqrt { \frac { 10 } { 3 } } : \sqrt { \frac { 5 } { 6 } }$$

Evaluate

$$2$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{10}{3}} as the division of square roots \frac{\sqrt{10}}{\sqrt{3}}.

$$\frac{\frac{\sqrt{10}}{\sqrt{3}}}{\sqrt{\frac{5}{6}}}$$

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

$$\frac{\frac{\sqrt{10}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{\sqrt{\frac{5}{6}}}$$

The square of \sqrt{3} is 3.

$$\frac{\frac{\sqrt{10}\sqrt{3}}{3}}{\sqrt{\frac{5}{6}}}$$

To multiply \sqrt{10} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\frac{\sqrt{30}}{3}}{\sqrt{\frac{5}{6}}}$$

Rewrite the square root of the division \sqrt{\frac{5}{6}} as the division of square roots \frac{\sqrt{5}}{\sqrt{6}}.

$$\frac{\frac{\sqrt{30}}{3}}{\frac{\sqrt{5}}{\sqrt{6}}}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\frac{\sqrt{30}}{3}}{\frac{\sqrt{5}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}}$$

The square of \sqrt{6} is 6.

$$\frac{\frac{\sqrt{30}}{3}}{\frac{\sqrt{5}\sqrt{6}}{6}}$$

To multiply \sqrt{5} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{\frac{\sqrt{30}}{3}}{\frac{\sqrt{30}}{6}}$$

Divide \frac{\sqrt{30}}{3} by \frac{\sqrt{30}}{6} by multiplying \frac{\sqrt{30}}{3} by the reciprocal of \frac{\sqrt{30}}{6}.

$$\frac{\sqrt{30}\times 6}{3\sqrt{30}}$$

Cancel out 3\sqrt{30} in both numerator and denominator.

$$2$$

Factor

$$2$$