Solve =1/2*(3sqrt{2}*frac{2sqrt{6}}{3})

$$= \frac { 1 } { 2 } \cdot ( 3 \sqrt { 2 } \cdot \frac { 2 \sqrt { 6 } } { 3 } )$$

Evaluate

$$2\sqrt{3}\approx 3.464101615$$

Solution Steps

Multiply \frac{1}{2} and 3 to get \frac{3}{2}.

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

Multiply \frac{3}{2} times \frac{2\sqrt{6}}{3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2\times 3 in both numerator and denominator.

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

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}.

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

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

$$2\sqrt{3}$$