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

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

Evaluate

$$\frac{\sqrt{15}}{3}\approx 1.290994449$$

Solution Steps

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

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

The square of \sqrt{6} is 6.

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

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

$$\frac{\sqrt{60}}{6}$$

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}.

$$\frac{2\sqrt{15}}{6}$$

Divide 2\sqrt{15} by 6 to get \frac{1}{3}\sqrt{15}.

$$\frac{1}{3}\sqrt{15}$$