Solve frac{7sqrt{3}-21}{14sqrt{3}}

$$\frac { 7 \sqrt { 3 } - 21 } { 14 \sqrt { 3 } }$$

Evaluate

$$\frac{1-\sqrt{3}}{2}\approx -0.366025404$$

Solution Steps

Rationalize the denominator of \frac{7\sqrt{3}-21}{14\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\left(7\sqrt{3}-21\right)\sqrt{3}}{14\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\left(7\sqrt{3}-21\right)\sqrt{3}}{14\times 3}$$

Multiply 14 and 3 to get 42.

$$\frac{\left(7\sqrt{3}-21\right)\sqrt{3}}{42}$$

Use the distributive property to multiply 7\sqrt{3}-21 by \sqrt{3}.

$$\frac{7\left(\sqrt{3}\right)^{2}-21\sqrt{3}}{42}$$

The square of \sqrt{3} is 3.

$$\frac{7\times 3-21\sqrt{3}}{42}$$

Multiply 7 and 3 to get 21.

$$\frac{21-21\sqrt{3}}{42}$$

Factor

$$\frac{1 - \sqrt{3}}{2} = -0.3660254037844386$$