Solve frac{2sqrt{3}}{sqrt{2}}+2sqrt{6}=

$$\frac { 2 \sqrt { 3 } } { \sqrt { 2 } } + 2 \sqrt { 6 } =$$

Evaluate

$$3\sqrt{6}\approx 7.348469228$$

Solution Steps

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

$$\frac{2\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+2\sqrt{6}$$

The square of \sqrt{2} is 2.

$$\frac{2\sqrt{3}\sqrt{2}}{2}+2\sqrt{6}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

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

Cancel out 2 and 2.

$$\sqrt{6}+2\sqrt{6}$$

Combine \sqrt{6} and 2\sqrt{6} to get 3\sqrt{6}.

$$3\sqrt{6}$$