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

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

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{5}{2}} as the division of square roots \frac{\sqrt{5}}{\sqrt{2}}.

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

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

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

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

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

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

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

The square of \sqrt{6} is 6.

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

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

$$\frac{\frac{\sqrt{10}}{2}}{\frac{\sqrt{30}}{6}}$$

Divide \frac{\sqrt{10}}{2} by \frac{\sqrt{30}}{6} by multiplying \frac{\sqrt{10}}{2} by the reciprocal of \frac{\sqrt{30}}{6}.

$$\frac{\sqrt{10}\times 6}{2\sqrt{30}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3\sqrt{10}}{\sqrt{30}}$$

Rationalize the denominator of \frac{3\sqrt{10}}{\sqrt{30}} by multiplying numerator and denominator by \sqrt{30}.

$$\frac{3\sqrt{10}\sqrt{30}}{\left(\sqrt{30}\right)^{2}}$$

The square of \sqrt{30} is 30.

$$\frac{3\sqrt{10}\sqrt{30}}{30}$$

Factor 30=10\times 3. Rewrite the square root of the product \sqrt{10\times 3} as the product of square roots \sqrt{10}\sqrt{3}.

$$\frac{3\sqrt{10}\sqrt{10}\sqrt{3}}{30}$$

Multiply \sqrt{10} and \sqrt{10} to get 10.

$$\frac{3\times 10\sqrt{3}}{30}$$

Multiply 3 and 10 to get 30.

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

Cancel out 30 and 30.

$$\sqrt{3}$$