Solve 2sqrt{3}*2*3+frac{sqrt{3}}{4}*(2sqrt{3})^2

$$2 \sqrt { 3 } \times 2 \times 3 + \frac { \sqrt { 3 } } { 4 } \times ( 2 \sqrt { 3 } ) ^ { 2 }$$

Evaluate

$$15\sqrt{3}\approx 25.980762114$$

Solution Steps

Multiply 2 and 2 to get 4.

$$4\times 3\sqrt{3}+\frac{\sqrt{3}}{4}\times \left(2\sqrt{3}\right)^{2}$$

Multiply 4 and 3 to get 12.

$$12\sqrt{3}+\frac{\sqrt{3}}{4}\times \left(2\sqrt{3}\right)^{2}$$

Expand \left(2\sqrt{3}\right)^{2}.

$$12\sqrt{3}+\frac{\sqrt{3}}{4}\times 2^{2}\left(\sqrt{3}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$12\sqrt{3}+\frac{\sqrt{3}}{4}\times 4\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$12\sqrt{3}+\frac{\sqrt{3}}{4}\times 4\times 3$$

Multiply 4 and 3 to get 12.

$$12\sqrt{3}+\frac{\sqrt{3}}{4}\times 12$$

Cancel out 4, the greatest common factor in 12 and 4.

$$12\sqrt{3}+3\sqrt{3}$$

Combine 12\sqrt{3} and 3\sqrt{3} to get 15\sqrt{3}.

$$15\sqrt{3}$$