Solve 2sqrt{3}*frac{12-sqrt{3}}{3}

$$2 \sqrt { 3 } \cdot \frac { 12 - \sqrt { 3 } } { 3 }$$

Evaluate

$$8\sqrt{3}-2\approx 11.856406461$$

Solution Steps

Express 2\times \frac{12-\sqrt{3}}{3} as a single fraction.

$$\frac{2\left(12-\sqrt{3}\right)}{3}\sqrt{3}$$

Use the distributive property to multiply 2 by 12-\sqrt{3}.

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

Express \frac{24-2\sqrt{3}}{3}\sqrt{3} as a single fraction.

$$\frac{\left(24-2\sqrt{3}\right)\sqrt{3}}{3}$$

Use the distributive property to multiply 24-2\sqrt{3} by \sqrt{3}.

$$\frac{24\sqrt{3}-2\left(\sqrt{3}\right)^{2}}{3}$$

The square of \sqrt{3} is 3.

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

Multiply -2 and 3 to get -6.

$$\frac{24\sqrt{3}-6}{3}$$