Solve -2sqrt{3}*1/2sqrt{3}

$$- 2 \sqrt { 3 } \cdot \frac { 1 } { 2 \sqrt { 3 } }$$

Evaluate

$$-1$$

Solution Steps

Rationalize the denominator of \frac{1}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Multiply 2 and 3 to get 6.

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

Cancel out 6, the greatest common factor in 2 and 6.

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

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

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

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

$$\frac{3}{-3}$$

Divide 3 by -3 to get -1.

$$-1$$

Factor

$$-1$$