Solve =frac{sqrt{12}}{sqrt{10}}

$$= \frac { \sqrt { 12 } } { \sqrt { 10 } }$$

Evaluate

$$\frac{\sqrt{30}}{5}\approx 1.095445115$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{2\sqrt{3}}{\sqrt{10}}$$

Rationalize the denominator of \frac{2\sqrt{3}}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

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

The square of \sqrt{10} is 10.

$$\frac{2\sqrt{3}\sqrt{10}}{10}$$

To multiply \sqrt{3} and \sqrt{10}, multiply the numbers under the square root.

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

Divide 2\sqrt{30} by 10 to get \frac{1}{5}\sqrt{30}.

$$\frac{1}{5}\sqrt{30}$$