Solve frac{sqrt{6}}{sqrt{31/5}}divsqrt{13/5}=

$$\frac { \sqrt { 6 } } { \sqrt { 3 \frac { 1 } { 5 } } } \div \sqrt { 1 \frac { 3 } { 5 } } =$$

Evaluate

$$\frac{5\sqrt{3}}{8}\approx 1.082531755$$

Solution Steps

Multiply 3 and 5 to get 15.

$$\frac{\frac{\sqrt{6}}{\sqrt{\frac{15+1}{5}}}}{\sqrt{\frac{1\times 5+3}{5}}}$$

Add 15 and 1 to get 16.

$$\frac{\frac{\sqrt{6}}{\sqrt{\frac{16}{5}}}}{\sqrt{\frac{1\times 5+3}{5}}}$$

Rewrite the square root of the division \sqrt{\frac{16}{5}} as the division of square roots \frac{\sqrt{16}}{\sqrt{5}}.

$$\frac{\frac{\sqrt{6}}{\frac{\sqrt{16}}{\sqrt{5}}}}{\sqrt{\frac{1\times 5+3}{5}}}$$

Calculate the square root of 16 and get 4.

$$\frac{\frac{\sqrt{6}}{\frac{4}{\sqrt{5}}}}{\sqrt{\frac{1\times 5+3}{5}}}$$

Rationalize the denominator of \frac{4}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\frac{\sqrt{6}}{\frac{4\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}}{\sqrt{\frac{1\times 5+3}{5}}}$$

The square of \sqrt{5} is 5.

$$\frac{\frac{\sqrt{6}}{\frac{4\sqrt{5}}{5}}}{\sqrt{\frac{1\times 5+3}{5}}}$$

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

$$\frac{\frac{\sqrt{6}\times 5}{4\sqrt{5}}}{\sqrt{\frac{1\times 5+3}{5}}}$$

Rationalize the denominator of \frac{\sqrt{6}\times 5}{4\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\frac{\sqrt{6}\times 5\sqrt{5}}{4\left(\sqrt{5}\right)^{2}}}{\sqrt{\frac{1\times 5+3}{5}}}$$

The square of \sqrt{5} is 5.

$$\frac{\frac{\sqrt{6}\times 5\sqrt{5}}{4\times 5}}{\sqrt{\frac{1\times 5+3}{5}}}$$

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

$$\frac{\frac{\sqrt{30}\times 5}{4\times 5}}{\sqrt{\frac{1\times 5+3}{5}}}$$

Multiply 4 and 5 to get 20.

$$\frac{\frac{\sqrt{30}\times 5}{20}}{\sqrt{\frac{1\times 5+3}{5}}}$$

Divide \sqrt{30}\times 5 by 20 to get \sqrt{30}\times \frac{1}{4}.

$$\frac{\sqrt{30}\times \frac{1}{4}}{\sqrt{\frac{1\times 5+3}{5}}}$$

Multiply 1 and 5 to get 5.

$$\frac{\sqrt{30}\times \frac{1}{4}}{\sqrt{\frac{5+3}{5}}}$$

Add 5 and 3 to get 8.

$$\frac{\sqrt{30}\times \frac{1}{4}}{\sqrt{\frac{8}{5}}}$$

Rewrite the square root of the division \sqrt{\frac{8}{5}} as the division of square roots \frac{\sqrt{8}}{\sqrt{5}}.

$$\frac{\sqrt{30}\times \frac{1}{4}}{\frac{\sqrt{8}}{\sqrt{5}}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{\sqrt{30}\times \frac{1}{4}}{\frac{2\sqrt{2}}{\sqrt{5}}}$$

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

$$\frac{\sqrt{30}\times \frac{1}{4}}{\frac{2\sqrt{2}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{30}\times \frac{1}{4}}{\frac{2\sqrt{2}\sqrt{5}}{5}}$$

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

$$\frac{\sqrt{30}\times \frac{1}{4}}{\frac{2\sqrt{10}}{5}}$$

Divide \sqrt{30}\times \frac{1}{4} by \frac{2\sqrt{10}}{5} by multiplying \sqrt{30}\times \frac{1}{4} by the reciprocal of \frac{2\sqrt{10}}{5}.

$$\frac{\sqrt{30}\times \frac{1}{4}\times 5}{2\sqrt{10}}$$

Multiply \frac{1}{4} and 5 to get \frac{5}{4}.

$$\frac{\sqrt{30}\times \frac{5}{4}}{2\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{30}\times \frac{5}{4}}{2\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{30}\times \frac{5}{4}\sqrt{10}}{2\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{30}\times \frac{5}{4}\sqrt{10}}{2\times 10}$$

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}.

$$\frac{\sqrt{10}\sqrt{3}\times \frac{5}{4}\sqrt{10}}{2\times 10}$$

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

$$\frac{10\times \frac{5}{4}\sqrt{3}}{2\times 10}$$

Multiply 2 and 10 to get 20.

$$\frac{10\times \frac{5}{4}\sqrt{3}}{20}$$

Express 10\times \frac{5}{4} as a single fraction.

$$\frac{\frac{10\times 5}{4}\sqrt{3}}{20}$$

Multiply 10 and 5 to get 50.

$$\frac{\frac{50}{4}\sqrt{3}}{20}$$

Reduce the fraction \frac{50}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{25}{2}\sqrt{3}}{20}$$

Divide \frac{25}{2}\sqrt{3} by 20 to get \frac{5}{8}\sqrt{3}.

$$\frac{5}{8}\sqrt{3}$$