Solve sqrt{2/13}divsqrt{5/6}

$$\sqrt { \frac { 2 } { 13 } } \div \sqrt { \frac { 5 } { 6 } }$$

Evaluate

$$\frac{2\sqrt{195}}{65}\approx 0.429668924$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{2}{13}} as the division of square roots \frac{\sqrt{2}}{\sqrt{13}}.

$$\frac{\frac{\sqrt{2}}{\sqrt{13}}}{\sqrt{\frac{5}{6}}}$$

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{\frac{\sqrt{2}\sqrt{13}}{\left(\sqrt{13}\right)^{2}}}{\sqrt{\frac{5}{6}}}$$

The square of \sqrt{13} is 13.

$$\frac{\frac{\sqrt{2}\sqrt{13}}{13}}{\sqrt{\frac{5}{6}}}$$

To multiply \sqrt{2} and \sqrt{13}, multiply the numbers under the square root.

$$\frac{\frac{\sqrt{26}}{13}}{\sqrt{\frac{5}{6}}}$$

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

$$\frac{\frac{\sqrt{26}}{13}}{\frac{\sqrt{5}}{\sqrt{6}}}$$

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

$$\frac{\frac{\sqrt{26}}{13}}{\frac{\sqrt{5}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}}$$

The square of \sqrt{6} is 6.

$$\frac{\frac{\sqrt{26}}{13}}{\frac{\sqrt{5}\sqrt{6}}{6}}$$

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

$$\frac{\frac{\sqrt{26}}{13}}{\frac{\sqrt{30}}{6}}$$

Divide \frac{\sqrt{26}}{13} by \frac{\sqrt{30}}{6} by multiplying \frac{\sqrt{26}}{13} by the reciprocal of \frac{\sqrt{30}}{6}.

$$\frac{\sqrt{26}\times 6}{13\sqrt{30}}$$

Rationalize the denominator of \frac{\sqrt{26}\times 6}{13\sqrt{30}} by multiplying numerator and denominator by \sqrt{30}.

$$\frac{\sqrt{26}\times 6\sqrt{30}}{13\left(\sqrt{30}\right)^{2}}$$

The square of \sqrt{30} is 30.

$$\frac{\sqrt{26}\times 6\sqrt{30}}{13\times 30}$$

To multiply \sqrt{26} and \sqrt{30}, multiply the numbers under the square root.

$$\frac{\sqrt{780}\times 6}{13\times 30}$$

Multiply 13 and 30 to get 390.

$$\frac{\sqrt{780}\times 6}{390}$$

Factor 780=2^{2}\times 195. Rewrite the square root of the product \sqrt{2^{2}\times 195} as the product of square roots \sqrt{2^{2}}\sqrt{195}. Take the square root of 2^{2}.

$$\frac{2\sqrt{195}\times 6}{390}$$

Multiply 2 and 6 to get 12.

$$\frac{12\sqrt{195}}{390}$$

Divide 12\sqrt{195} by 390 to get \frac{2}{65}\sqrt{195}.

$$\frac{2}{65}\sqrt{195}$$