Solve frac{1-sqrt{3}}{4sqrt{3}}

$$\frac { 1 - \sqrt { 3 } } { 4 \sqrt { 3 } }$$

Evaluate

$$\frac{\sqrt{3}-3}{12}\approx -0.105662433$$

Solution Steps

Rationalize the denominator of \frac{1-\sqrt{3}}{4\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\left(1-\sqrt{3}\right)\sqrt{3}}{4\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\left(1-\sqrt{3}\right)\sqrt{3}}{4\times 3}$$

Multiply 4 and 3 to get 12.

$$\frac{\left(1-\sqrt{3}\right)\sqrt{3}}{12}$$

Use the distributive property to multiply 1-\sqrt{3} by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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