Solve frac{sqrt{6}}{sqrt{10}}

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

Evaluate

$$\frac{\sqrt{15}}{5}\approx 0.774596669$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{6}}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

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

The square of \sqrt{10} is 10.

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

To multiply \sqrt{6} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{60}}{10}$$

Factor 60=2^{2}\times 15. Rewrite the square root of the product \sqrt{2^{2}\times 15} as the product of square roots \sqrt{2^{2}}\sqrt{15}. Take the square root of 2^{2}.

$$\frac{2\sqrt{15}}{10}$$

Divide 2\sqrt{15} by 10 to get \frac{1}{5}\sqrt{15}.

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