Solve 2sqrt{6}*frac{sqrt{3}}{4}

$$2 \sqrt{ 6 } \times \frac{ \sqrt{ 3 } }{ 4 }$$

Evaluate

$$\frac{3\sqrt{2}}{2}\approx 2.121320344$$

Solution Steps

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

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

Express \frac{\sqrt{3}}{2}\sqrt{6} as a single fraction.

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

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

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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