Solve sqrt{31/5}divsqrt{15/5}

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

Evaluate

$$\frac{2\sqrt{10}}{5}\approx 1.264911064$$

Solution Steps

Multiply 3 and 5 to get 15.

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

Add 15 and 1 to get 16.

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

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

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

Calculate the square root of 16 and get 4.

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

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

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

The square of \sqrt{5} is 5.

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

Multiply 1 and 5 to get 5.

$$\frac{\frac{4\sqrt{5}}{5}}{\sqrt{\frac{5+5}{5}}}$$

Add 5 and 5 to get 10.

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

Divide 10 by 5 to get 2.

$$\frac{\frac{4\sqrt{5}}{5}}{\sqrt{2}}$$

Express \frac{\frac{4\sqrt{5}}{5}}{\sqrt{2}} as a single fraction.

$$\frac{4\sqrt{5}}{5\sqrt{2}}$$

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

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

The square of \sqrt{2} is 2.

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

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

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

Multiply 5 and 2 to get 10.

$$\frac{4\sqrt{10}}{10}$$

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

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