Solve 1/2*2*sqrt{3}frac{sqrt{6}}{3}

$$\frac{ 1 }{ 2 } \times 2 \times \sqrt{ 3 } \frac{ \sqrt{ 6 } }{ 3 }$$

Evaluate

$$\sqrt{2}\approx 1.414213562$$

Solution Steps

Cancel out 2 and 2.

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

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

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

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}.

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

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

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

Cancel out 3 and 3.

$$\sqrt{2}$$