Solve 1/2*6sqrt{8}*4*frac{sqrt{3}}{2}

$$\frac { 1 } { 2 } \cdot 6 \sqrt { 8 } \cdot 4 \cdot \frac { \sqrt { 3 } } { 2 }$$

Evaluate

$$12\sqrt{6}\approx 29.393876913$$

Solution Steps

Multiply 4 and 6 to get 24.

$$24\times \frac{1}{2}\sqrt{8}\times \frac{\sqrt{3}}{2}$$

Multiply 24 and \frac{1}{2} to get \frac{24}{2}.

$$\frac{24}{2}\sqrt{8}\times \frac{\sqrt{3}}{2}$$

Divide 24 by 2 to get 12.

$$12\sqrt{8}\times \frac{\sqrt{3}}{2}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$12\times 2\sqrt{2}\times \frac{\sqrt{3}}{2}$$

Multiply 12 and 2 to get 24.

$$24\sqrt{2}\times \frac{\sqrt{3}}{2}$$

Cancel out 2, the greatest common factor in 24 and 2.

$$12\sqrt{3}\sqrt{2}$$

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

$$12\sqrt{6}$$