Solve 2sqrt{6}*frac{sqrt{2}}{4}

$$2 \sqrt { 6 } \cdot \frac { \sqrt { 2 } } { 4 }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

Solution Steps

Cancel out 4, the greatest common factor in 2 and 4.

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

Express \frac{\sqrt{2}}{2}\sqrt{6} as a single fraction.

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

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Cancel out 2 and 2.

$$\sqrt{3}$$